Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 29c

Chapter 10, Problem 29c

(c) Room temperature is often assumed to be 25 °C. Calculate the molar volume of an ideal gas at 25 °C and 101.3 kPa pressure.

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Convert the temperature from degrees Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = 25 + 273.15 \).

Use the ideal gas law equation \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Rearrange the ideal gas law to solve for the molar volume \( V_m \), which is the volume per mole: \( V_m = \frac{RT}{P} \).

Substitute the values into the equation: \( R = 8.314 \text{ J/mol·K} \), \( T \) is the temperature in Kelvin from step 1, and \( P = 101.3 \text{ kPa} \).

Calculate the molar volume \( V_m \) using the rearranged equation and the substituted values to find the volume in liters per mole.

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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 an ideal 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 allows us to calculate the behavior of gases under various conditions.

Molar Volume

Molar volume is defined as the volume occupied by one mole of a substance at a given temperature and pressure. For an ideal gas at standard temperature and pressure (0 °C and 101.3 kPa), the molar volume is approximately 22.4 L. However, at different conditions, such as 25 °C and 101.3 kPa, the molar volume can be calculated using the Ideal Gas Law.

Temperature Conversion

In gas calculations, temperature must be expressed in Kelvin rather than Celsius. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. For example, 25 °C is equivalent to 298.15 K. This conversion is crucial for accurately applying the Ideal Gas Law and obtaining correct results.

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02:10

Temperature Conversion Example

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Textbook Question

Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is x kPa. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1x. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

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Textbook Question

(b) What is the molar volume of an ideal gas at STP?

Textbook Question

(b) If a car tire is filled to a pressure of 220.6 kPa measured at 24 °C, what will be the tire pressure if the tires heat up to 49 °C during driving?

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Textbook Question

(d) If you measure pressure in bars instead of atmospheres, calculate the corresponding value of R in L-bar/mol-K.

Textbook Question

Suppose you are given two 2-L flasks and told that one contains a gas of molar mass 28, the other a gas of molar mass 56, both at the same temperature and pressure. The mass of gas in the flask A is 1.0 g and the mass of gas in the flask B is 2.0 g. Which flask contains the gas of molar mass 28, and which contains the gas of molar mass 56?

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