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Chapter 5: Problem 33

What volume will 5.6 moles of sulfur hexafluoride \(\left(\mathrm{SF}_{6}\right)\) gas occupy if the temperature and pressure of the gas are \(128^{\circ} \mathrm{C}\) and \(9.4 \mathrm{~atm} ?\)

Short Answer

Expert verified
The volume is approximately 19.6 liters.

Step by step solution

01

Convert Temperature to Kelvin

First, convert the temperature from degrees Celsius to Kelvin using the formula: \[ T(K) = T(掳C) + 273.15 \]Plug in the given temperature:\[ T(K) = 128 + 273.15 = 401.15 \, \text{K} \]
02

Use the Ideal Gas Law

The ideal gas law equation is \[ PV = nRT \]where\( P \) = pressure in atm = 9.4 atm, \( V \) = volume in liters, \( n \) = number of moles = 5.6 moles, \( R \) = ideal gas constant = 0.0821 \, \mathrm{L} \, \mathrm{atm} \, \mathrm{mol}^{-1} \, \mathrm{K}^{-1}, \( T \) = temperature in Kelvin = 401.15 K.
03

Solve for Volume

Rearrange the ideal gas law to solve for volume \( V \):\[ V = \frac{nRT}{P} \]Substitute the known values:\[ V = \frac{5.6 \, \text{mol} \times 0.0821 \, \mathrm{L} \, \mathrm{atm} \, \mathrm{mol}^{-1} \, \mathrm{K}^{-1} \times 401.15 \, \mathrm{K}}{9.4 \, \mathrm{atm}} \]Calculate the volume:\[ V \approx \frac{5.6 \times 0.0821 \times 401.15}{9.4} \approx 19.6 \, \text{liters} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Temperature Conversion
To properly apply the ideal gas law, it is essential to work with temperatures in the Kelvin scale. This is because Kelvin is an absolute temperature scale that starts at absolute zero. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature.
For instance, if the temperature is 128掳C, convert it to Kelvin as follows:
  • Add 273.15 to the given Celsius temperature: 128 + 273.15 = 401.15 K.
This formula ensures that we are working with absolute temperatures, allowing for accurate calculations of gas behavior under varying conditions.
Moles and Gas Volume
The ideal gas law ties in the number of moles of gas to its volume. This relationship is represented in the formula:
  • \( PV = nRT \)
Where:
  • P is the pressure in atmospheres (atm),
  • V is the volume in liters (L),
  • n is the number of moles of the gas,
  • R is the ideal gas constant,
  • T is the temperature in Kelvin (K).
Understanding the influence of moles on gas volume is essential. The more moles of gas you have under constant temperature and pressure, the larger the volume the gas will occupy. This is because gas molecules spread out to fill the space they are in. Thus, according to our exercise, 5.6 moles of sulfur hexafluoride at 9.4 atm and 401.15 K would fill approximately 19.6 liters.
Ideal Gas Constant
In the ideal gas law, the ideal gas constant (R) acts as the proportionality constant that relates the pressure, volume, temperature, and moles of a gas. For calculations with pressure in atmospheres and volume in liters, the value of R is usually 0.0821 L atm mol鈦宦� K鈦宦�.
This constant allows us to bridge the other variables in the equation, providing a reliable way to predict how gas behaves when changes occur in conditions such as pressure, temperature, or volume.
  • Using the constant in calculations ensures you obtain accurate and consistent results, particularly in standard chemistry problems involving gases.
By applying this reliable constant, the ideal gas law becomes a powerful tool for solving many real-world problems involving gases, as evidenced by solving for the volume in our exercise.

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Most popular questions from this chapter

Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases?

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Define Dalton's law of partial pressures and mole fraction. Does mole fraction have units?

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