Introduction to Chemistry: Step-by-Step Study Guidance

Q1. How many moles of gas are in a 5.0 L sample at 2.0 atm and 300 K?

Background

Topic: Ideal Gas Law

This question tests your ability to use the ideal gas law to determine the number of moles of a gas given its pressure, volume, and temperature.

Key Terms and Formulas

• Ideal Gas Law: $PV = nRT$

• P = pressure (atm)

• V = volume (L)

• n = number of moles

• R = ideal gas constant ($0.0821\ \mathrm{L\cdot atm\cdot mol^{-1}\cdot K^{-1}}$)

• T = temperature (K)

Step-by-Step Guidance

1. Identify the known values: $P = 2.0\ \mathrm{atm}$, $V = 5.0\ \mathrm{L}$, $T = 300\ \mathrm{K}$, $R = 0.0821\ \mathrm{L\cdot atm\cdot mol^{-1}\cdot K^{-1}}$.

2. Write the ideal gas law equation: $PV = nRT$.

3. Rearrange the equation to solve for $n$: $n = \frac{PV}{RT}$.

4. Plug in the known values into the rearranged equation, making sure all units are correct.

Try solving on your own before revealing the answer!

Final Answer: 0.41 mol

$n = \frac{(2.0)(5.0)}{(0.0821)(300)} \approx 0.41$ mol

By substituting the values into the ideal gas law and solving, you find the number of moles in the sample.