To perform the given operation and express in scientific notation, need to subtract 5.00x10^4 from 7.00x10^5.
Step 1: Perform the subtraction:
7.00x10^5 - 5.00x10^4 = 700,000 - 50,000 = 650,000Step 2: Determine the appropriate scientific notation for the result.
The result, 650,000, can be expressed in scientific notation as 6.50x10^5.
To represent this in the requested format, we need to determine the exponent and adjust the coefficient accordingly.
The original coefficient, 6.50, can be written as 6.50x10^5.
Therefore, the answer in scientific notation is 6.50x10^5.
The simplest approach to express a huge value is with scientific notation. In scientific notation, a number is divided into two pieces.
The numbers (the decimal point will come after the first number)
10 (the power that positions the decimal point correctly)
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1. Identify each of the following as a measurements of length,area, volume, mass, density, time or temperature:
a)ns
b)10.0 kg/m3
c) 1.2 pm
d)750 km2
e) 83 K
f) 4.0 mm3
2. Carry out the following operations, and express the answerwith the appropriate number of significant figures and units:
a) (5.231 mm)(6.1 mm)
b) 72.3 g/1.5 mL
c) 12.21 g + 0.0132 g
d) 31.03 g + 12 mg
3. Drug medications are often prescribed on the basis of bodyweight. The adult dosage of Elixophyllin, a drug used to treatasthma, is 6 mg/kg of body mass. Calculate the dose in milligramsfor a 150-lb person.
4. A man who is 5 ft. 8 in. tall weighs 160 lb. What is hisheight in centimeters and his mass in kilograms.
In the same way, as the U.S. customary system employs feet, quarts, and ounces to measure these things, the metric system measures length, liquid volume, and mass in units like meter, liter, and gram.
The metric system uses kilograms or grams to measure mass, meters or kilometers to measure distance, and liters to measure volume. Time doesn't have any quantifiable physical qualities. The length of time between two events is what we are actually counting. People have used a variety of methods throughout history to keep track of the passage of time, including sunrise and sunset times and moon phases. Volume, which is measured in cubic units, is the area in three dimensions that matter occupies or that is encircled by a surface. The cubic meter (m3), a derivation of the SI unit of volume.
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will mark brainliest!!
The following data was collected when a reaction was performed experimentally in the laboratory.
Reaction Data
Reactants Products
Fe2O3 Al Al2O3 Fe
Starting Amount in Reaction 3 moles 5 moles ? ?
Determine the maximum amount of Fe that was produced during the experiment. Explain how you determined this amount.
The maximum amount of Fe that was produced during the experiment is 3 moles.
This can be determined by using the law of conservation of mass which states that the total mass of the reactants is equal to the total mass of the products. The starting amount of reactants is 3 moles of Fe2O3 and 5 moles of Al. The reaction produces Al2O3 and Fe. So, in order to balance the equation, the moles of Fe produced must be equal to the moles of Fe2O3 that were consumed.
Fe2O3 + 2Al -> Al2O3 + 2Fe
Since 3 moles of Fe2O3 were used, the maximum amount of Fe that can be produced is 3 moles.
Answer: 2.5 moles of Fe
Explanation:
Balanced Equation: Fe2O3 + 2AI ---> 2Fe + AI2O3
Mole Ratios:
- for FE2O3: (1mol Fe / 1mol Fe2O3)
- for AI: (1mol Fe / 2mol AI)
Stoichiometry Equation for Each Reactant:
- (3mol Fe2O3 / 1) x (1mol Fe / 1mol Fe2O3)
- (3/1) x (1mol Fe/1)
- 3mol Fe
- (5mol AI / 1) x (1mol Fe / 2mol AI)
- (5/1) x (1mol Fe/2)
- 2.5mol Fe
The maximum amount of Fe that can be produced is 2.5 moles; as AI is the limiting reactant
What would the mass be, in grams, of 1.99 x 1024 molecules of P4010?
Avogadro's constant says that 1 mole of any atom [tex]6.022*10^2^3[/tex] contains atoms. In this case, you have [tex]1.99 * 10^2^4[/tex] atoms:
[tex]1.99*10^2^4/6.022*10^2^3=3.3[/tex]
1 mole of p4010 = 283.889
So [tex]1.99* 10^2^4[/tex] molecules mass is
[tex]283.889*3.3=936.833 gram[/tex]
Therefore, the mass in grams, of 1.99 x 1024 molecules of P4010 is 936.833 grams.
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What is an ionic bond with two suitable examples explain the difference between an ionic and a covalent bond?
Covalent bonds are created between two nonmetals, whereas ionic bonds are formed between a metal and a nonmetal.
Covalent bonds between atoms develop when there is little to no difference in the electronegativity of the atoms, whereas ionic bonds form when there is a large difference.
Covalent bonds are created when the half-filled atomic orbitals of two different atoms overlap, but ionic bonds cannot be created by overlapping orbitals.
For example, the ionic bond in NaCl is written as Na⁺Cl⁻ because sodium is a metal and chlorine is a non-metal.
Let's use methane as an example. Due to the low difference in electronegativity between carbon and hydrogen, the atomic orbitals of these two elements meet in this molecule and form a covalent bond.
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What type of epithelium is found along most of the digestive tract?
In humans, simple columnar epithelium is the type of epithelium that found along most of the digestive tract including the stomach, and intestines.
Simple columnar epithelium is made up of a single layer of tall, slender columnar epithelial cells with oval-shaped nuclei that are linked to the basement membrane in the basal region. The majority of the digestive tract's organs in humans, including the stomach and intestines, are lined by simple columnar epithelium. The uterus is lined with simple columnar epithelium as well.
There are two further classifications for simple columnar epithelium: ciliated and non-ciliated (glandular). Tiny hairs on the ciliated portion of the simple columnar epithelium assist in moving mucus and other materials along the respiratory system.
The majority of the human digestive tract, including the stomach and intestines, is lined by simple columnar epithelium.
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What is the pressure of a mixture of nitrogen carbon dioxide and oxygen?
The pressure of a mixture of nitrogen, carbon dioxide, and oxygen gases (PO₂ = 254 mm Hg, PN₂ = 0.351 atm, and PCO₂ = 43.9 kPa) is 113.3 kPa
The total pressure exerted by a gas mixture is the sum of the partial pressures of the component gases. For example, Earth's atmosphere is a mixture of gases consisting of nitrogen, oxygen, argon, carbon dioxide, and other gases. Partial pressure is the pressure that each gas has in a mixture so that the pressure of each gas is not affected by the presence of other gases.
The partial pressure formula is:
Ptotal = PNitrogen + Poxygen + PCarbon dioxide.
In question:
PO₂ 254 mm Hg = 33.9 kPa
PN₂ 0.351 atm = 35.5 kPa
PCO₂ = 43.9 kPa
So,
Ptotal = PO₂ + PN₂ + PCO₂
Ptotal = 33.9 kPa + 35.5 kPa + 43.9 kPa
Ptotal = 113.3 kPa
The pressure of a mixture of nitrogen, carbon dioxide and oxygen gases are 113.3 kPa.
Complete the question:
What is the pressure of a mixture of nitrogen carbon dioxide and oxygen gases if the pressures of these gases are as follows: PO2 = 254 mm Hg, PN2 = 0.351 ATM, and PCO2 = 43.9 kPa?
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Draw a chiral alcohol with the formula C4H10O.
t-Butyl alcohol (t-BuOH) is a tertiary aliphatic alcohol used as a solvent or alcohol denaturant and as a fragrance carrier in cosmetics. t-butyl alcohol is one of the chiral forms of alcohol.
t-BuOH was reported as an ingredient in 32 eye makeup, fragrance, and shaving formulations at concentrations between 0.00001% and 0.3%. Common modifiers found in cosmetics and personal care products include:
Denatonium benzoate, t-butyl alcohol, diethyl phthalate, methyl alcohol. The alcohol denaturation process does not chemically change the ethanol molecule. Acute exposure:
Acute exposure to tert-butyl alcohol can cause eye irritation and redness, runny nose, sore throat, headache, nausea, fatigue, dizziness, and red and dry skin. The formula of this chiral alcohol is C4H10O.
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the number of objects in a mole of something is dictated by which constant? One mole of a substance is equal to 6.022 xd7 10xb3 units of that substance (such as atoms, molecules, or ions). The number 6.022 xd7 10xb3 is known as Avogadro’s number or Avogadro’s constant. The concept of the mole can be used to convert between mass and number of particles.. Created by Sal Khan.a. trueb. false
The number of objects in a mole of something is dictated by Avogadro's constant and the given statement is TRUE.
One mole of a substance is equal to 6.022 x 10^23 units of that substance (such as atoms, molecules, or ions), and this number is known as Avogadro's number or Avogadro's constant. The concept of the mole is a unit of measurement used in chemistry to express amounts of a chemical substance. It is defined as the amount of a substance that contains the same number of entities (such as atoms, molecules, or ions) as there are in 12 grams of pure carbon-12. Avogadro's constant, 6.022 x 10^23, is used to relate the number of entities in a substance to the number of moles of that substance. This allows for the conversion between mass and number of particles, as well as for the calculation of the number of entities in a given mass of a substance.
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Balance the following equations
1. N2O5 -> N2O4 + O2
2. KNO3 -> KNO2 + O2
3. NH4NO2 -> N2 + H2O
4. O3 -> O2
5. Zn + AgCl -> ZnCl2 + Ag
6. NaOH + H2SO4 -> NA2SO4 + H2O
The following are the balanced chemical equations: 1). 2N2O5 -> 2N2O4 + 1O2, 2). 2KNO3 -> 2KNO2 + O2, 3). NH4NO2 -> N2 + 2H2O, 4).2O3 -> 3O2, 5). Zn + 2AgCl -> ZnCl2 + 2Ag, 6). 2NaOH + H2SO4 -> Na2SO4 + 2H2O.
Which five chemical equations are there?Synthesis, breakdown, single replacement, doubling replacement, and combustion are the five main categories of chemical reactions. One material is created from several reactants in a composition reaction.
What are class 10 chemical equations?A chemical equation is a symbol- and formula-based valid expression of a chemical reaction, with the reactant entities given on the left side and the resultant entities given on the right. Examples are NaOH+HClNaCl+H2O.
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What is the new volume when an expandable 4.51 L container of gas at 273 K is warmed to 546 K? V = [?] L
It will now be 8.3L in volume.
Volume explain: What is it?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume is measured in cubic units.
What are volume and what is its unit?Volume is the three-dimensional space inhabited by matter or encompassed by a surface, and it is measured in cubic units. The cubic meter (m3), a derived unit, is the SI unit of volume.
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Answer: the answer is 9.02
Explanation:
I figured the answer out because 273 x 2 equals 546 so I thought you had to multiply 4.51 x 2 and the answer is 9.02
How many molecules of carbon dioxide are released during one turn of the citric acid cycle?
Match the appropriate benefit of dietary fiber intake to its associated disease. (Use each choice only once). Cardiovascular Disease A. Lowers Blood Cholesterol Hypertension B. Lowers Blood Pressure Type 2 Diabetes c. Decreases intestinal transit time and exposure to potential toxins Constipation D. Slows absorption of glucose Obesity E Slows rate of digestion, promotes satiety Colon Cancer F. Increases fecal bulk & promotes regularity
Cardiovascular diseases (CVDs) are the most common cause of death worldwide, claiming the lives of an estimated 17.9 million persons each year. CVDs are a group of heart and blood disorders.
How is blood made in the human body?The bone marrow produces stem cells, the building blocks that the body uses to make the different blood cells – red cells, white cells and platelets. The erythropoietin sends a message to the stem cells telling more of them to develop into red blood cells, rather than white cells or platelets.
What is in human blood?Whole blood is made up of red blood cells, white blood cells and platelets, all of which are suspended in a liquid called plasma. Whole blood and each of it's four components are all valuable tools in modern medicine.
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PLEASEE HELPP ASAPPP IM DYING HERE HAHA PLSS :(
Decomposition - 5
Combustion - 3
Synthesis - 4
Double replacement - 1
Single replacement - 2
Decomposition reaction is the breaking down of one reactant into multiple substances/fragments/parts due to external sources of energy.
Combustion is the burning of any material and we know that burning is a reaction with oxygen.
Synthesis is the formation of one compound from multiple reactants i.e. one product.
A double replacement or double displacement reaction takes place like this: AB + CD --> AC + BD
In single displacement reactions, one element is substituted for another element in the final compound, i.e. A + CD --> AC + D
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what is the percentage mass of oxygen of magnesium nitrate with working
Answer:
below on my bule
Explanation:bule
The circumference of a circle is 11π cm. What is the area, in square centimeters? Express your answer in terms of \piπ
The circumference of a circle is 11π cm. Then the area is 30.25 π cm.
What do you mean by area ?The term area is defined as the region bounded by the shape of an object. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
The area of a shape is the measurement of its surface. To calculate the area of a rectangle or square, multiply the length and width of the rectangle or square.
C = pi d
Therefore,
11π cm = diameter
Radius is 1/2 the diameter
Then radius = 5.5π cm
Area = πr²
Area = 30.25 π
Thus, The circumference of a circle is 11π cm. Then the are is 30.25 π cm.
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Element Molar mass (\pu{g/mol}g/molg, slash, m, o, l)
\ce{H}HH 1.0081.0081, point, 008
\ce{C}CC 12.0112.0112, point, 01
\ce{O}OO 16.0016.0016, point, 00
Using the information in the table, calculate the number of moles in a \pu{5.73 kg}5.73 kg5, point, 73, space, k, g sample of lactic acid (\ce{C3H6O3}CX
3
HX
6
OX
3
).
The number of moles in the 5.73 Kg sample of lactic acid, C₃H₆O₃, is 63.61 moles
How do I determine the number of moles in the sample?The relationship between number of mole and molar mass is given below:
Number of mole = mass / molar mass
With the above formula, we can obtain the number of mole in the 5.73 Kg sample of lactic acid, C₃H₆O₃. Details below:
Molar mass of H = 1.008 g/molMolar mass of C = 12.01 g/molMolar mass of O = 16 g/molMolar mass of C₃H₆O₃ = (12.01 × 3) + (1.008 × 6) + (16 × 3) = 36.03 + 6.048 + 48 = 90.078 g/molMass of C₃H₆O₃ = 5.73 Kg = 5.73 × 1000 = 5730 gNumber of mole of C₃H₆O₃ =?Mole = mass / molar mass
Number of mole of C₃H₆O₃ = 5730 / 90.078
Number of mole of C₃H₆O₃ = 63.61 moles
Thus, the number of mole of the lactic acid, C₃H₆O₃ is 63.61 moles
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How many moles of magnesium is 3.01 x 1022 formula units of magnesium?
Answer:
So 3.01 times 10 to the 22 atoms is 050 moles magnesium
Explanation:
hope this helps
Transfer of lactase to pH 5 results in a substantial decrease in enzyme activity, likely due to the disruption of
The enzyme's secondary, tertiary, and quaternary structures are probably disrupted when lactase is transferred to pH 5, which causes a significant drop in enzyme activity.
Which one of these could lead to the denature of a protein?Protein denaturation can be brought on by a wide variety of substances and circumstances, including heat, chemical molecules, pH changes, and heavy metal ions.Lactase activity benefits from a pH of 6. The enzyme's secondary, tertiary, and quaternary structures are probably disrupted when lactase is transferred to pH 5, which causes a significant drop in enzyme activity.The enzyme's secondary, tertiary, and quaternary structures are probably disrupted when lactase is transferred to pH 5, which causes a significant drop in enzyme activity.To learn more about lactase refer to:
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Titanium (IV) oxide (TiO2) is a white substance that is produced by reaction between the mineral ilmenite (FeTiO3) and sulfuric acid:
FeTiO3 + H2SO4 -> TiO2 + FeSO4 + H2O
In one process 8.00 X10 3 kg of FeTiO3 yielded 3. 67 X 103 kg of TiO2. What is the yield of the reaction?
Sulfuric acid reacts with the mineral ilmenite to form titanium(IV) oxide (TiO2), a white material. The reaction has a Percentage of yield 76.3%.
What is Percentage of yield ?The amount of product actually made compared with the maximum calculated yield is called the percentage yield.
The amount of product produced by a chemical reaction is known as the real yield.The amount of product derived from a stoichiometric or balanced equation utilizing the limiting reactant to calculate product is known as the theoretical yield.Actual yield/Theoretical yield*100
FeTiO3 + H2SO4 -> TiO2 + FeSO4 + H2O
Molar mass of FeTiO3 = 152 g / mole
Number of mole of FeTiO3 = Mass / molar mass
= 8.65 x 10³ / 152
= 56907 g / mole
By solving the equation
Number of moles of TiO2 = 56907 g / mole
Mass of TiO2 = molar mass x number of moles
= 80 x 56907
= 4552560 = 4.55 x 10³
Percent yield = 3.47 x 10³ / 4.55 x 10³ x 100
= 0.763 x 100
= 76.3 %
Thus, Titanium(IV) oxide (TiO2) is a white substance produced by the action of sulfuric acid on the mineral ilmenite. The percent yield of the reaction is 76.3%.
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Which reaction would not occur as written due to the Activity Series of Metals (found in your Chemistry Reference Table)?
A. 3 Mg + 2 AlCl3 --> 3 MgCl2 + 2 Al
B. Al + NaCl --> AlCl3 + Na
C. Ca + CuCl2 --> CaCl2 + Cu
D. 2 K + 2 H2O --> 2 KOH + H2
The reaction Al + NaCl → AlCl₃ + Na among the given reactions will not occur according to the reactivity series. Therefore, option B is correct.
What is reactivity series?The reactivity series of metals can be described as the arrangement of metals in the decreasing order of their reactivities.
The metals at the top of the activity series are strong reducing agents as they can easily oxidize. These metals easily corrode. The reducing ability gets weaker moving down the series.
The electropositive elements reduce as move down the activity series of metals. All metals above hydrogen in the reactivity series emit hydrogen gas upon reacting with dilute HCl.
Aluminum metal lies down to the sodium metal so it can not displace sodium metal therefore, this reaction is not possible.
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all ________ are metazoans.
All species of life are metazoans. Eukaryotes with several cells and mitochondria are called metazoan animals.
What makes animals metazoans?All multicellular organisms with differentiated body parts, including tissues and organs, belong to the Metazoa group. They have specialized cells lining the cavity of their digestive system. They have nucleated cells with cell membranes.
How can you recognize a metazoan?The majority of metazoans have bilateral symmetry. They display the division of labor. The body organization of lower invertebrates is at the tissue or organ level, whereas the body organization of larger invertebrates and vertebrates is at the organ-system level. Unlike protozoans, which have a cell wall, animals don't.
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Once the two atoms are bonded together, can you move the two atoms as a pair?
draw the line-angle structural formula for cyclopropane
The line angle structure formula for cyclopropane is C3H6 or (CH2)3 with three methylene groups attached at the corner of a triangle.
The cycloalkane, cyclopropane has the chemical formula (CH2)3, and it is made up of three methylene groups (CH2) that are joined together to create a ring. The structure experiences significant ring strain as a result of the ring's modest size. The structure of cycloprane is depicted in the image attached.
A line-angle formula, also known as a skeletal structure, is even more condensed. In this formula, carbon atoms are implied at the corners and ends of lines, and each carbon atom is assumed to be connected to enough hydrogen atoms to give it four bonds. This is because carbon atom has a valency of four or it is a tetravalent atom.
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. A carbocation is all of the following, except
O a positively charged species.
O a reactive intermediate.
O an electrophile.
O a nucleophile.
A carbocation is all of the following, except a nucleophile.A carbocation is a positively charged species, a reactive intermediate, and an electrophile, but it is not a nucleophile.
Nucleophiles are species that donate electrons to form a new covalent bond, while electrophiles are species that accept electrons to form a new covalent bond. Carbocation have a positive charge and therefore it is an electrophile.A carbocation is a type of organic cation in which a carbon atom has a positive charge. Carbocations are formed by the removal of a leaving group from an organic molecule, such as an alkane, alkyl halide, or alkyne, creating a positively charged carbon atom. Carbocations are typically intermediate species in organic reactions and are highly reactive, as the positive charge on the carbon atom creates a high degree of electron deficiency.
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Draw a chiral ketone with the formula C6H12O.
One of the chiral ketones which has the formula of C₆H₁₂O is Methyl isobutyl ketone
MIBK is used as a solvent in factories that manufacture paints, rubber products, chemicals, and machinery. As a solvent, it is used in pesticide spraying. Pharmaceutical companies that manufacture prescription drugs also use his MIBK. MIBK enhances and retains flavor and aroma.
Unlike acetone and butanone, MIBK has fairly low solubility in water. It has similar polarity to ethyl acetate but is more acid/base stable. This and its low density make it suitable for liquid-liquid extraction. These are the uses and applications of one of the chiral ketones.
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When the following reactions come to equilibrium, does the equilibrium mixture contain mostly reactants or mostly products?
H2 (g) + S (s) <--> H2S (g) Kc = 7.8 x 105
N2 (g) + 2H2 (g) <--> N2H4 (g) Kc = 7.4 x 10-26
Is large, the equilibrium mixture is mostly products. If Kc is small, the equilibrium mixture is mostly reactants. When Kc is approximately 1, the equilibrium mixture contains appreciable amounts of both reactants and products.
What is equilibrium?Equilibrium is the state in which market supply and demand balance each other, and as a result prices become stable. Generally, an over-supply of goods or services causes prices to go down, which results in higher demand—while an under-supply or shortage causes prices to go up resulting in less demand.The balancing effect of supply and demand results in a state of equilibrium.The equilibrium price is where the supply of goods matches demand. When a major index experiences a period of consolidation or sideways momentum, it can be said that the forces of supply and demand are relatively equal and the market is in a state of equilibrium.Economists find that prices tend to fluctuate around the equilibrium levels. If the price rises too high, market forces will incentivize sellers to come in and produce more. If the price is too low, additional buyers will bid up the price. These activities keep the equilibrium level in relative balance over time.To learn more about momentum refer to:
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What is the Law of
Conservation of Mass?
A. The total mass of the products will always
be equal to the total mass of the reactants.
B. The total mass of the products will always
be more than the total mass of the reactants.
C. The total energy of the products will
always be equal to the total energy of the
reactants.
D. The total mass of the products will always
be less than the total mass of the reactants.
A 25.0 g piece of brass at 325 °C was placed into a sample of water. The final temperature of the water and brass was 42.0 °C. How much energy is released by the brass?
The energy released by the brass is an example of the heat of fusion.
How much energy is released by the brass?The heat released by the brass can be calculated using the equation:q = m × c × ΔTwhere q is the amount of energy released (in Joules), m is the mass of the brass (25.0 g), c is the specific heat capacity of brass (0.385 J/g•°C), and ΔT is the change in temperature (325 °C - 42.0 °C = 283 °C).Therefore, the energy released by the brass is:q = (25.0 g) × (0.385 J/g•°C) × (283 °C)q = 29,202.5 JHeat of fusion is the amount of energy released or absorbed when a substance changes from a solid to a liquid or vice versa. In this case, the brass is changing from a solid to a liquid and releasing energy in the process. The energy released can be calculated using the formula: q = m·ΔT·c, where q is the heat of fusion, m is the mass of the brass, ΔT is the change in temperature, and c is the specific heat capacity of the brass.The mass of the brass is 25.0 g. The change in temperature is 325 °C - 42.0 °C, or 283 K. The specific heat capacity of brass is 0.387 J/g·K. Plugging these values into the equation gives us a heat of fusion of 2,969.2 joules. This is the amount of energy released by the brass when it changed from a solid to a liquid.To learn more about The mass of the brass refer to:
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Answer:
-283 C
Explanation:
I got it right
Choose the correct IUPAC name for the following bicyclic compound.
A. 2-fluorobicyclo[2.2.1]hexane
B. 2-fluorobicyclo[2.1.1]hexane
C 5-fluorobicyclo[2.1.1]hexane
D. 6-fluorobicyclo[2.1.1]hexane
E. 3-fluorobicyclo[2.2.0]pentane
F. 4-fluorobicyclo[2.1.0Jpentane A
The correct IUPAC name of bicyclic compound is option no.4 (1alpha,4alpha)-5alpha-Fluorobicyclo[2.1.0]pentane.
The molecular formula of this compound is C₅H₇F and the molecular weight of this compound is 86.11. It has a 3D conformer.
IUPAC nomenclature is a method of naming organic chemical compounds which is recommended by the applied chemistry or the international union of pure. IUPAC names sometimes very simpler than the older names, as with ethanol instead of ethyl alcohol. For a relatively simple molecules they can be more easily understood than to the non-systematic names, which must be learnt as well as looked over. It should have maximum number of multiple bonds, maximum length as well as number of single bonds.
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The height of a cylinder with a radius of 4 cm is increasing at a rate of 2 centimeters per minute. Find the rate of change of the volume with respect to time when the height is 10 centimeters.
The rate of change of the volume with respect to time is 32π cm³/min. To find the rate of change of the volume with respect to time, we need to take the derivative of the volume function with respect to time, which is denoted by dV/dt.
The formula for the volume of a cylinder is V = πr²2h, where r is the radius and h is the height. To find the rate of change of the volume with respect to time, we need to find the derivative of V with respect to t.
Let's call h(t) the height of the cylinder at time t, so it is increasing at a rate of 2 cm/min.
dV/dt = d/dt (πr²h(t)) = πr²2 dh/dt = π(4²)(2) = 32π cm³/min
When the height is 10 cm, the rate of change of the volume with respect to time is 32π cm³/min.
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