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The heat capacity at constant pressure of an ideal gas is defined as:

[tex]C_p = \left(\frac{\partial H}{\partial T}\right)_P = \left(\frac{\partial (U + PV)}{\partial T}\right)_P[/tex]

What is the pressure (in bars) exerted by 1.00 mol of CH\(_4\)(g) that occupies a 250-mL container at 0°C? Assume methane is an ideal gas in this case.
(R = 0.082058 L atm/K-mol = 8.3145 J/K-mol; 1 atm = 1.01325 bar)

A. 97.8 bar
B. 78.6 bar
C. 89.6 bar
D. 90.8 bar

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QUESTION 14
Which of the following is NOT a characteristic of an ideal gas?

A. There are no interactions experienced except for random and elastic collisions.
B. The particles have volume.
C. The movement of the particles is completely random and independent of one another.
D. An ideal gas is composed of point particles.

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The compressibility factor, Z → 1 for a real gas when:

A. V = 1 dm³
B. V → ∞
C. P → 0
D. P increases

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QUESTION 16
The observation that [tex]Z = \frac{P_cV_c}{RT_c}[/tex] is approximately equal to 0.3 for all gases demonstrates the:

A. First Law of Thermodynamics
B. Law of Conservation of Mass
C. Law of Corresponding States
D. Law of Conservation of Energy

Answer :

The pressure exerted by 1.00 mol of CH4 in a 250 mL container at 0°C is 8.452 bar.

Assume methane is an ideal gas in this case.

(R = 0.082058 L atm/K-mol = 8.3145 J/K-mol;

1 atm = 1.01325 bar)

We know that P V = n R T We can calculate pressure as:

P = n R T / V= (1.00 mol) (0.082058 L atm / K mol) (273.15 K) / (0.25 L)

= 8.348 atm Pressure in bar can be calculated as:

1 atm = 1.01325 bar

Therefore, P = 8.348 atm x 1.01325 bar/atm ≈ 8.452 bar

The option "The particles have volume" is NOT a characteristic of an ideal gas. An ideal gas is defined as a theoretical gas composed of a set of randomly-moving point particles that are not subject to inter-particle collisions. The volume of each particle is assumed to be zero. The other options given in the question are all characteristics of an ideal gas. The observation that Z = PcVcnRTc is approximately equal to 0.3 all gases demonstrates the Law of Corresponding States. The Law of Corresponding States states that the behavior of all real gases becomes similar at the same reduced conditions, which are defined as pressure, volume, and temperature relative to the gas' critical values.

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