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Ch.10 - Gases
All textbooksBrown 14th EditionCh.10 - GasesProblem 93
Chapter 10, Problem 93

In Sample Exercise 10.16, we found that one mole of Cl2 confined to 22.41 L at 0 °C deviated slightly from ideal behavior. Calculate the pressure exerted by 1.00 mol Cl2 confined to a smaller volume, 5.00 L, at 25 °C. (a) Use the ideal gas law for the calculation. (b) Then use the van der Waals equation for your calculation. (Values for the van der Waals constants are given in Table 10.3.) (c) Why is the difference between the result for an ideal gas and that calculated using the van der Waals equation greater when the gas is confined to 5.00 L compared to 22.41 L?

Verified step by step guidance
1
Step 1: Start with the ideal gas law equation, which is given by PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
Step 2: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For 25 °C, T = 25 + 273.15 = 298.15 K.
Step 3: Substitute the known values into the ideal gas law equation: n = 1.00 mol, V = 5.00 L, R = 0.0821 L·atm/mol·K, and T = 298.15 K. Solve for P, the pressure.
Step 4: For the van der Waals equation, use the formula \((P + \frac{an^2}{V^2})(V - nb) = nRT\), where a and b are van der Waals constants for Cl2. Look up these constants in Table 10.3.
Step 5: Substitute the known values and constants into the van der Waals equation and solve for P. Compare the pressure obtained from the ideal gas law and the van der Waals equation to understand why the difference is greater at 5.00 L.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law assumes that gas particles do not interact and occupy no volume, making it a useful approximation under many conditions.
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Van der Waals Equation

The Van der Waals equation is an adjustment of the Ideal Gas Law that accounts for the volume occupied by gas molecules and the attractive forces between them. It is expressed as (P + a(n/V)²)(V - nb) = nRT, where 'a' and 'b' are constants specific to each gas. This equation provides a more accurate description of real gas behavior, especially at high pressures and low temperatures, where deviations from ideality are significant.
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Real Gas Behavior

Real gases deviate from ideal behavior due to intermolecular forces and the finite volume of gas particles. At high pressures and low volumes, such as in the case of 5.00 L, these effects become more pronounced, leading to greater discrepancies between the predictions of the Ideal Gas Law and the Van der Waals equation. Understanding these deviations is crucial for accurately predicting gas behavior in various conditions.
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Related Practice
Textbook Question

The planet Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between 600 K and 700 K and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

Textbook Question

Which statement concerning the van der Waals constants a and b is true? (a) The magnitude of a relates to molecular volume, whereas b relates to attractions between molecules. (b) The magnitude of a relates to attractions between molecules, whereas b relates to molecular volume. (c) The magnitudes of a and b depend on pressure. (d) The magnitudes of a and b depend on temperature.

Textbook Question
Based on their respective van der Waals constants( Table 10.3), is Ar or CO2 expected to behave more nearlylike an ideal gas at high pressures?
Textbook Question

Calculate the pressure that CCl4 will exert at 80 °C if 1.00 mol occupies 33.3 L, assuming that (a) CCl4 obeys the ideal-gas equation (b) CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.)

Textbook Question

Calculate the pressure that CCl4 will exert at 80 °C if 1.00 mol occupies 33.3 L, assuming that (c) Which would you expect to deviate more from ideal behavior under these conditions, Cl2 or CCl4? Explain.

Textbook Question

Table 10.3 shows that the van der Waals b parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section 7.3. Is the van der Waals radius we calculate from the b parameter of Table 10.3 more closely associated with the bonding or nonbonding atomic radius discussed there? Explain.