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MAXImum [283]
3 years ago
8

When 229.0 J of energy is supplied as heat to 3.00 mol of Ar(g) at constant pressure the temperature of the sample increases by

2.55 K. Assuming that in the experiment the gas behaves as an ideal gas, calculate the molar heat capacities at constant volume and at constant pressure of Ar(g).
Chemistry
1 answer:
bazaltina [42]3 years ago
5 0

Answer:

The molar heat capacity at constant volume is 21.62 JK⁻¹mol⁻¹

The molar heat capacity at constant pressure is 29.93 JK⁻¹mol⁻¹

Explanation:

We can calculate the molar heat capacity at constant pressure from

C_{p,m} = \frac{C_{p} }{n}

Where C_{p,m} is the molar heat capacity at constant pressure

{C_{p} } is the heat capacity at constant pressure

and n is the number of moles

Also {C_{p} } is given by

{C_{p} } = \frac{\Delta H}{\Delta T}

Hence,

C_{p,m} = \frac{C_{p} }{n} becomes

C_{p,m} = \frac{\Delta H }{n \Delta T}

From the question,

\Delta H = 229.0 J

n = 3.00 mol

\Delta T = 2.55 K

Hence,

C_{p,m} = \frac{\Delta H }{n \Delta T} becomes

C_{p,m} = \frac{229.0}{(3.00) (2.55)}

C_{p,m} = 29.93 JK⁻¹mol⁻¹

This is the molar heat capacity at constant pressure

For, the molar heat capacity at constant volume,

From the formula

C_{p,m} = C_{v,m} + R

Where C_{v,m} is the molar heat capacity at constant volume

and R is the gas constant (R = 8.314 JK⁻¹mol⁻¹)

Then,

C_{v,m} = C_{p,m}  - R

C_{v,m} = 29.93 - 8.314

C_{v,m} = 21.62 JK⁻¹mol⁻¹

This is the molar heat capacity at constant volume

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