The molar heat capacity of a certain substance varies with temperature according to the empirical equation C=29.5J/(mol⋅K)+(8.20×10−3J/(mol⋅K2))T How much heat is necessary to change the temperature of 3.00 mol of this substance from 27∘C to 227∘C ? (Hint: Use the equation dQ=nCdT and integrate.)

Answers

Answer 1

Answer:

The quantity of heat necessary to change the temperature of 3.00 mol of the substance from 27°C to 227°C is 19.668 KJ

Explanation:

From the question, The empirical equation is

C=29.5J/(mol⋅K)+(8.20×10−3J/(mol⋅K2))T

[tex]C=29.5J/(mol.K)+(8.20\times 10^{-3} J/(mol.K^{2} ))T[/tex]

Now, to determine the heat necessary to change the temperature of 3.00 mol of this substance from 27∘C to 227∘C, that is ΔQ

From, dQ=nCdT

Integrating both sides, we get

[tex]\int\limits^ {Q_{2}} _{Q_{1}} {dQ} \, = \int\limits^ {T_{2} }_{T_{1} } nC \, dT[/tex]

[tex]{Q_{2}} -{Q_{1}} = \int\limits^ {T_{2} }_{T_{1} } n[ {29.5J/(mol.K)+(8.20\times 10^{-3} J/(mol.K^{2} ))T} \, ]dT[/tex]

[tex]\Delta Q = \int\limits^ {T_{2} }_{T_{1} } 3.00mol[ {29.5J/(mol.K)+(8.20\times 10^{-3} J/(mol.K^{2} ))T} \, ]dT[/tex]

[tex]\Delta Q = \int\limits^ {T_{2} }_{T_{1} } [ {88.5J/K+ (24.6\times 10^{-3} J/K^{2} )T} \, ]dT[/tex]

[tex]\Delta Q = \int\limits^ {T_{2} }_{T_{1} } {88.5J/KdT + \int\limits^ {T_{2} }_{T_{1} } 24.6\times 10^{-3} J/K^{2} T} dT[/tex]

[tex]\Delta Q =(88.5J/K )\int\limits^ {T_{2} }_{T_{1} } dT + (24.6\times 10^{-3} J/K^{2})\int\limits^ {T_{2} }_{T_{1} } T} dT[/tex]

(NOTE: [tex]\int {dx} = x[/tex] and [tex]\int\ {x} \, dx = \frac{x^{2} }{2}[/tex] )

Hence, we get

[tex]\Delta Q =(88.5J/K )({T_{2} }-{T_{1} )+ (24.6\times 10^{-3} J/K^{2}) (\frac{T_{2}^{2} }{2} - \frac{T_{1}^{2} }{2} )[/tex]

From the question, [tex]T_{1}[/tex] = 27 °C = (27+273) K = 300K

Also, [tex]T_{2}[/tex] = 227 °C = (227+273) K = 500K

Then,

[tex]\Delta Q =(88.5J/K )(500K - 300K )+ (24.6\times 10^{-3} J/K^{2}) (\frac{(500K)^{2} }{2} - \frac{(300K)^{2} }{2} )[/tex]

[tex]\Delta Q =(88.5J/K )(200K )+ (24.6\times 10^{-3} J/K^{2}) (80\times 10^{3} K^{2} )[/tex]

[tex]\Delta Q =17700J +1968J \\[/tex]

[tex]\Delta Q =19668J[/tex]

[tex]\Delta Q =19.668KJ[/tex]

Hence, the quantity of heat necessary to change the temperature of 3.00 mol of the substance from 27°C to 227°C is 19.668 KJ

(NOTE: KJ means Kilo Joules)


Related Questions

How many moles are there in 45.0 g of SF6?

Answers

Answer:

0.31 mole

Explanation:

The following data were obtained from the question:

Mass of SF6 = 45.0 g

Number of mole of SF6 =..?

Next, we shall determine the molar mass of SF6.

This can be obtained as follow:

Molar mass of SF6 = 32 + (19×6)

Molar mass of SF6 = 32 + 114

Molar mass of SF6 = 146 g/mol

Finally, we shall determine the number of mole in 45 g of SF6 as follow:

Molar mass of SF6 = 146 g/mol

Mass of SF6 = 45.0 g

Number of mole of SF6 =..?

Number of mole = mass /Molar mass

Number of mole of SF6 = 45 /146

Number of mole of SF6 = 0.31 mol

Therefore, 0.31 mol is present in 45 g of SF6.

How much Ca(NO3)2 should be weighed out to have 0.650 mol?A) 66.4 g.B) 97.68.C) 107 g.D) 133 g.E) 165 g.

Answers

Answer:

C) 107 g

Explanation:

Step 1: Calculate the molar mass of Ca(NO₃)₂

We can calculate the molar mass of Ca(NO₃)₂ by adding the masses of its elements.

M = 1 × Ca + 2 × N + 2 × 3 × O

M = 1 × 40.08 g/mol + 2 × 14.01 g/mol + 6 × 16.00 g/mol

M = 164.10 g/mol

Step 2: Calculate the mass corresponding to 0.650 moles of Ca(NO₃)₂

We multiply the number of moles by the molar mass.

0.650 mol × 164.10 g/mol = 107 g

What mass of sodium hydroxide will completely neutralize 2.5 mol of sulfuric acid?

Answers

Given :

2.5 mole of Sulfuric acid [tex]( H_2SO_4 )[/tex] .

To Find :

Mass of sodium hydroxide will completely neutralize 2.5 mol of sulfuric acid

Solution :

Let us assume volume of water be 1 L .

Now , we know , to neutralize 1 mole of sulfuric acid we need 2 moles of NaOH .

So , for 2.5 mole sulfuric acid required 5 mole of NaOH .

Moles of NaOH ,

[tex]n=M\times Volume \\\\n=5\times 1=5\ moles[/tex]  

Molecular mass of NaOH , M.M = 58.44 g/mol .

Mass of 5 moles of NaOH :

[tex]m=5\times 58.44\ g\\\\m=292.2\ g[/tex]

Hence , this is the required solution .


7. Why is the d-block one energy level behind the s-block? Also, why would the f-block be so far behind?

Answers

Answer:

7. Why is the d-block one energy level behind the s-block? Also, why would the f-block be so far behind?

me to

Explanation:

An atom has 14 protons, 16 neutrons, and 14 electrons. What is its mass number?

Answers

The answer is 30.

Explanation:

The total number of protons and neutrons in a nucleus is called mass number. So 14 proton plus 16 neutron is = 30 mass number.

Which of the following is equivalent to 251 torr?
A. 0.330 atm.
B. 1900 atm.
C. 29.4 psi.
D. All of these choices.

Answers

Answer:

Option A. 0.330 atm.

Explanation:

To know the correct answer, we simply do the following:

1. Conversion of 251 torr to atm

760 torr = 1 atm

Therefore,

251 torr = 251 torr / 760 torr × 1 atm

251 torr = 0.330 atm

2. Conversion of 251 torr to psi

1 torr = 0.0193 psi

Therefore,

250 torr = 250 torr / 1 torr × 0.0193 psi

250 torr = 4.825 psi

From the above illustrations, 251 torr is equivalent to both 0.330 atm and 4.825 psi. Therefore, only option A is correct.

In the firs reaction of glycolysis, glucose is converted to _________. The phosphate comes from __________.
A __________ is an enzyme that transfers the terminal phosphate of _________ to a substrate. The product of this reaction is then ______________ to fructose-6-phosphate.
Fructose-6-phosphate is then phosphorylated by a second __________ reaction, giving ___________.

Answers

Answer:

EMP Pathway - Embden Meyerhof Parnas Pathway

Answer:

glucose 6-phosphate; ATP

kinase; ATP; isomerized

kinase; fructose 1,6-bisphosphate

Explanation:

Which is a representation of a compound that gives the number of atoms and types of atoms in that compound?

Answers

that uses chemical symbols to indicate the types of atoms followed by subscripts to show the number of atoms of each type in the molecule.

Using a ruler, you measure the length of a rectangle to be 12.75 cm and the width to be 3.64 cm. Calculate the area of this rectangle

Answers

Answer:

46.41 cm

Explanation:

Area is length times width. Multiply 12.75 by 3.64 to get your answer. Don't forget to label it as cm!

Air should be classified as:
Element
Compound
Homogeneous mixture
Heterogeneous mixture

Answers

Answer:

element

Explanation:

it is use full for you thanks

What is a Pure element ?

Answers

A substance where almost all have the same atomic number of protons

What tool do you use to measure mass?

Answers

Answer: Balance

Explanation:  Mass is the amount of matter contained in a body.

A good experimental design should always:

Answers

Answer:

A good experimental design should always: include more than one independent variable. have predictable outcomes. be repeatable.

Explanation:

Hope this helps :D

.
What volume of 10M NaOH would you need to add to a vessel, if your final
solution is 200 mL of 0.1M NaOH?

Answers

Answer:

2 mL

Explanation:

Step 1: Given data

Initial concentration (C₁): 10 MInitial volume (V₁): ?Final concentration (C₂): 0.1 MFinal volume (V₂): 200 mL

Step 2: Calculate the volume of the 10 M solution

We want to prepare a diluted solution from a concentrated one. we can calculate the volume of the initial solution using the dilution rule.

C₁ × V₁ = C₂ × V₂

V₁ = C₂ × V₂/C₁

V₁ = 0.1 M × 200 mL/10 M

V₁ = 2 mL

Calculate the density of the following objects:

a. A box with a mass of 1500 grams that occupies 7600 mL of space.
Please help! will mark you as brainliesy

Answers

Answer:

Density =M/V

1500/7600

5.0666666667=Ans...


7. Change the following data into scientific notation:
a. The distance between Pluto and the Sun is 5,913,000 km.
b. The density of nitrogen gas is 0.0012506 g/cm3.

Answers

Explanation:

A number can be written in the form of scientific notation as follows :

[tex]N=x\times 10^y[/tex]

x is any real number and y is integer

(a) The distance between Pluto and the Sun is 5,913,000 km.

There are 6 digits after 5. In scientific form is given by :

[tex]N=5.91\times 10^6\ km[/tex]

(b) The density of nitrogen gas is 0.0012506 g/cm³.

There are 2 digits before 1. In scientific notation,

[tex]d=1.25\times 10^{-3}\ g/cm^3[/tex]

All measurements contain errors. Averaging the measurements reduces the error. A graph can also reduce error when the line is drawn through the center of the data. A student measured the mass and volume of 5 different pieces of the same metal, plotted the data and obtained a slope of 8.90 g/mL. How did you know that the metal was copper and not nickel? (Describe a different way to identify that the metal is copper).

Answers

Answer:

See explanation

Explanation:

The slope of a graph in which mass was plotted against volume is the density of the object. Density of objects have been measured and recorded in standard handbooks for the purpose of reference. If the density of an unknown substance is measured, it can now be compared with the density of known substances recorded in standard handbooks such as the handbook of physics and chemistry. By so doing, the unknown substance can be identified.

According to standard handbooks, the density of copper is 8.96 g/ml while that of nickel is 8.908 g/ml. If the average slope obtained is around 8.96 g/ml, then the metal is copper and not nickel.

An alternative to this method is to measure the refractive index of the piece of metal and compare the average values observed with the contents of standard handbooks in order to identify the unknown metal.

The combustion of palmitic acid is represented by the chemical equation: C16H32O2(s) + 23O2(g) → 16 CO2(g) + 16 H2O(l) The magnitude of ΔrU is ____________ in comparison to the magnitude of ΔrH a. The same b. Smaller c. Greater d. Need additional information

Answers

Answer:

The correct option is C

Explanation:

From the question we are told that

The reaction is

[tex]C_{16}H_{32}O_2(g) + 23O_2(g) \to 16 CO_2(g) + 16 H_2O(l)[/tex]

Generally [tex]\Delta H = \Delta U + \Delta N* RT[/tex]

Here [tex]\Delta H[/tex] is the change in enthalpy

[tex]\Delta U [/tex] is the change in the internal energy

              [tex] \Delta N[/tex]  is the difference between that number of moles of product and the number of moles of reactant

Looking at the reaction we can discover that the elements that was consumed and the element that was formed is [tex] O_2[/tex] and  [tex]CO_2[/tex] and this are both gases so the change would occur in the number of moles

So  

[tex]\Delta H = \Delta U + [16 -23]* RT[/tex]

[tex]\Delta H = \Delta U -7RT[/tex]

The  negative sign in the equation tell us that the enthalpy[tex]\Delta_r H[/tex] would be less than the Internal energy [tex]\Delta_r U[/tex]

At elevated temperatures, methylisonitrile (CH3NC) converts to acetonitrile (CH3CN): CH3NC(g) --> CH3CN(g) At the start of the experiment, there are 0.200 mol of reactant (CH3NC) and 0 mol of product (CH3CN) in the reaction vessel. After 25 min of reaction, 0.108 mol of reactant (CH3NC) remain. The average rate of decomposition of methyl isonitrile, CH3NC, in this 25 min period is __________ mol/min. A. 3.7 x 10-3 B. 0.092 C. 2.3 D. 4.3 x 10-3 E. 0.54

Answers

Answer:

A. 3.7 x 10⁻³

Explanation:

In the beginning of the reaction there are 0.200 moles of reactant. After 25 minutes, remain 0.108 moles. That means the moles that wer descomposed are:

0.200 moles - 0.108 moles = 0.092 moles of reactant were descomposed.

That descomposition occurs in 25 minutes. The average rate of descomposition in moles / minute are:

0.092 moles Methyl isonitrile / 25 minutes = 3.7x10⁻³ mol/min.

Right option is:

A. 3.7 x 10⁻³

Which acid and its conjugate base would be the best buffer at pH=7.5?

Answers

Answer:

HEPES.

Explanation:

Hello,

In this case, considering the given options, and the pH requirement of 7.5, considering the Henderson-Hasselbach equation:

[tex]pH=pKa+log(\frac{[base]}{[acid]})[/tex]

The best buffer is that having the closest pKa to the required pH, thus, for the given Ka, we obtain:

[tex]pKa_{MES}=-log(Ka_{MES})=-log(7.9x10^{-7})=6.10\\\\pKa_{HEPES}=-log(Ka_{HEPES})=-log(3.2x10^{-8})=7.49\\\\pKa_{Formic \ acid}=-log(Ka_{Formic \ acid})=-log(1.8x10^{-4})=3.74\\\\pKa_{Acetic\ acid}=-log(Ka_{Acetic\ acid})=-log(1.8x10^{-5})=4.74\\\\pKa_{Tris}=-log(Ka_{Tris})=-log(6.3x10^{-9})=8.2[/tex]

Therefore, the best buffer is the HEPES since its pKa is almost the required pH.

Regards-

Which of the following features describe your graph? Check all that apply. appropriate title of graph showing the effect of changing temperature on the volume of a gas appropriate axes titles time on the x-axis as the independent variable temperature on the y-axis as the dependent variable data sets are all at equal intervals on each axis range on both axes cover data points in such a way that there is not too much extra space on the graph

Answers

Answer:

you'll be fine if you mark all or one, it's really up to you

Explanation:

did it on edgenuity

What is the mass of 12.83 mL of acetic acid (98% wt/wt)?

Answers

Answer:

The mass of the acetic acid is 13.5 g

Explanation:

Given;

weight percent of the acetic acid (ratio of solute to total solution), w/w = 98 %

volume of acetic acid, v = 12.83 mL

density of acetic acid, ρ = 1.05 g/mL

density is given by;

density = mass / volume

mass = density x volume

mass of the acetic acid in 12.83 mL =  1.05 g/mL x 12.83 mL

mass of the acetic acid in 12.83 mL = 13.5 g

Therefore, the mass of the acetic acid is 13.5 g

CC14
Element
Compound
Which one is it

Answers

I think the answer is Compound.

Which statement below regarding evaporation is not correct?A. When a liquid is first placed in a closed container, the evaporation rate is higher than it is in an open container under the same conditions. B. When a liquid is first placed in a closed container, the evaporation rate is higher than the condensation rate. C. When the rates of evaporation and condensation are equal, the system has reached dynamic equilibrium. D. Vapor pressure refers to the pressure of a gas at a given temperature in equilibrium with its liquid phase. E. Stronger intermolecular forces within the liquid typically result in a lower vapor pressure under a given set of conditions.

Answers

Answer:

A. When a liquid is first placed in a closed container, the evaporation rate is higher than it is in an open container under the same conditions.

Explanation:

Evaporation refers to the process by which a liquid changes to gas or vapor. It usually occurs at the surface of a liquid.

Factors that affects evaporation include; nature of the liquid, surface area of liquid exposed, temperature and wind.

Considering the options given:

A. When a liquid is first placed in a closed container, the evaporation rate is higher than it is in an open container under the same conditions. = False

This is false because, the more the surface of the liquid exposed, the higher the rate of evaporation.

B. When a liquid is first placed in a closed container, the evaporation rate is higher than the condensation rate. = True

This is true because when a liquid is first placed in a container, the equilibrium position favors evaporation initially than condensation as saturation of the space above the liquid with vapor has not been achieved.

C. When the rates of evaporation and condensation are equal, the system has reached dynamic equilibrium.= True

Dynamic equilibrium is achieved when the rate of forward and backward reaction, in this case, evaporation and condensation are equal.

D. Vapor pressure refers to the pressure of a gas at a given temperature in equilibrium with its liquid phase. = True

E. Stronger intermolecular forces within the liquid typically result in a lower vapor pressure under a given set of conditions.  = True

Strong intermolecular forces between the molecules of the liquid causes the liquid to remain in the liquid state rather than turning to vapor, thereby lowering vapor pressure

Definition of the word derived?

Answers

Answer:

obtain something from (a specified source).

Explanation:

Answer:

It is like the orgins of something

For the following reaction, 2.45 grams of methane (CH4) are allowed to react with 27.7 grams of carbon tetrachloride . methane (CH4)(g) + carbon tetrachloride(g) dichloromethane (CH2Cl2)(g) What is the maximum mass of dichloromethane (CH2Cl2) that can be formed? grams What is the FORMULA for the limiting reagent? What mass of the excess reagent remains after the reaction is complete? grams

Answers

Answer:

The limiting reactant is CH₄

26.0g of CH₂Cl₂ is the maximum amount that can be formed

4.15g CCl₄ will remain

Explanation:

The reaction of methane, CH₄, with carbon tetrachloride, CCl₄ is:

CH₄ + CCl₄ → 2CH₂Cl₂

To find the maximum mass of dichloromethane that can be determined we need to find moles of methane and carbon tetrachloride:

Moles CH₄:

2.45g * (1mol / 16.04g) = 0.153 moles

Moles CCl₄:

27.7g * (1mol / 153.82g) = 0.180 moles

That means just 0.153 moles of CCl₄ will react until CH₄ is over.

The limiting reactant is CH₄

Assuming the whole 0.153 moles will react, the moles of CH₂Cl₂ will be:

0.153 moles CH₄ * (2 moles CH₂Cl₂ / 1 mole CH₄) = 0.306 moles of CH₂Cl₂

The mass is (Molar mass dichloromethane: 84.93g/mol):

0.306 moles of CH₂Cl₂  * (84.93g / mol) = 26.0g of CH₂Cl₂

The moles of CCl₄ that remain are:

0.180 moles - 0.153 moles = 0.027 moles

In grams:

0.027 moles * (153.82g / mol) = 4.15g CCl₄

Classify each reactant and product in this reaction as an acid or base according to the Brønsted theory.
HF + H2O = F + H30+


Answer Bank
HF
H30+
F-
H2O

Answers

Answer:

Reaction: [tex]\rm HF + H_2O \rightleftharpoons F^{-} + H_3O^{+}[/tex].

[tex]\rm HF[/tex]: Bronsted-Lowry Acid.[tex]\rm H_3O^{+}[/tex]: Bronsted-Lowry conjugate Acid of [tex]\rm F^{-}[/tex]: Bronsted-Lowry conjugate Base of [tex]\rm HF[/tex].[tex]\rm H_2O[/tex]: Bronsted-Lowry Base.

Explanation:

In the Bronsted-Lowry acid-base theory, the acid in a reaction is the species that loses a proton, [tex]\rm H^{+}[/tex]. The resultant species would be the conjugate base of that acid.

On the other hand, the Bronsted-Lowry base in a reaction is the species that accepts a proton [tex]\rm H^{+}[/tex]. The resultant species would be the conjugate acid of that base.

Identify the conjugate acid-base pairs in this reaction. Note that the two species in each pair are related by the gain or loss of a single proton. Therefore, their formula should look similar to each other.

For this reaction, [tex]\rm HF[/tex] and [tex]\rm F^{-}[/tex], as well as [tex]\rm H_2O[/tex] and [tex]\rm H_3O^{+}[/tex] form two similar-looking reactant-product pairs:

The reactant [tex]\rm HF[/tex] loses one proton to form the product [tex]\rm F^{-}[/tex]. Therefore, [tex]\rm HF\![/tex] would be the Bronsted-Lowry acid, while [tex]\rm F^{-}\![/tex] would be its conjugate base.The reactant [tex]\rm H_2O[/tex] gains one proton to form the product [tex]\rm H_3O^{+}[/tex]. Therefore, [tex]\rm H_2O\![/tex] would be the Bronsted-Lowry base, while [tex]\rm H_3O^{+}\![/tex] would be the conjugate acid.

Why should an experiment be replicated

Answers

an experiment should be replicated for one: it my give more reason to people who did not do it them selves two: during the experiment one variable could have been wrong like a gust of wind or a draft that's why you should conduct the experiment 3 to 4 times then get the medium or the average of your results giving you a more accurate answer.

What are the derived SI units?

Answers

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

Draw the structure of 4-methyl-5-oxohexanal.

Answers

Answer:

Explanation:

The structural formula provides more information which is often used to represent a particular organic substance. A structural formula indicates how the atoms are arranged within the molecule of a substance. From the information, the structure of  4-methyl-5-oxohexanal is represented by using a stick formula where the methyl group falls into position 4 and oxygen group falls into position 5 on the hexanal compound.

The structure is provided in the image attached below for better understanding.

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