Ideal Gas Law Practice Worksheet with five word problems to solve using the ideal gas law.

Let's solve each problem using the Ideal Gas Law, which is:

$$
PV = nRT
$$

Where:
- $ P $ = pressure (in atm)
- $ V $ = volume (in liters, L)
- $ n $ = number of moles
- $ R $ = ideal gas constant = 0.0821 L·atm/(mol·K)
- $ T $ = temperature (in Kelvin, K)

---

Problem 1:

How many moles of gas does it take to occupy 120 liters at a pressure of 2.3 atmospheres and a temperature of 340 K?

Given:
- $ V = 120 \text{ L} $
- $ P = 2.3 \text{ atm} $
- $ T = 340 \text{ K} $
- $ R = 0.0821 \text{ L·atm/(mol·K)} $

We need to find $ n $.

$$
n = \frac{PV}{RT}
= \frac{(2.3)(120)}{(0.0821)(340)}
= \frac{276}{28.014}
\approx 9.85 \text{ moles}
$$

✔ Answer: Approximately 9.85 moles

---

Problem 2:

If I have a 50 liter container that holds 45 moles of gas at a temperature of 200°C, what is the pressure inside the container?

First, convert temperature to Kelvin:
- $ T = 200^\circ C + 273 = 473 \text{ K} $

Given:
- $ V = 50 \text{ L} $
- $ n = 45 \text{ mol} $
- $ T = 473 \text{ K} $
- $ R = 0.0821 $

Solve for $ P $:

$$
P = \frac{nRT}{V}
= \frac{(45)(0.0821)(473)}{50}
= \frac{1802.78}{50}
= 36.06 \text{ atm}
$$

✔ Answer: Approximately 36.06 atmospheres

---

Problem 3:

It is not safe to put aerosol canisters in a campfire, because the pressure inside the canisters gets very high and they can explode. If I have a 1.0 liter canister that holds 2 moles of gas, and the campfire temperature is 1400°C, what is the pressure inside the canister?

Convert temperature:
- $ T = 1400^\circ C + 273 = 1673 \text{ K} $

Given:
- $ V = 1.0 \text{ L} $
- $ n = 2 \text{ mol} $
- $ T = 1673 \text{ K} $

$$
P = \frac{nRT}{V}
= \frac{(2)(0.0821)(1673)}{1.0}
= (0.1642)(1673)
= 274.0 \text{ atm}
$$

✔ Answer: Approximately 274 atmospheres

> ⚠️ This is extremely high — dangerous! That’s why aerosol cans shouldn’t be heated.

---

Problem 4:

How many moles of gas are in a 30-liter scuba canister if the temperature of the canister is 300 K and the pressure is 200 atmospheres?

Given:
- $ V = 30 \text{ L} $
- $ P = 200 \text{ atm} $
- $ T = 300 \text{ K} $

$$
n = \frac{PV}{RT}
= \frac{(200)(30)}{(0.0821)(300)}
= \frac{6000}{24.63}
\approx 243.6 \text{ moles}
$$

✔ Answer: Approximately 243.6 moles

---

Problem 5:

I have a balloon that can hold 100 liters of air. If I blow up this balloon with 3 moles of oxygen gas at a pressure of 1 atmosphere, what is the temperature of the balloon?

Given:
- $ V = 100 \text{ L} $
- $ n = 3 \text{ mol} $
- $ P = 1 \text{ atm} $

Solve for $ T $:

$$
T = \frac{PV}{nR}
= \frac{(1)(100)}{(3)(0.0821)}
= \frac{100}{0.2463}
\approx 406.0 \text{ K}
$$

Convert to Celsius:
- $ T = 406 - 273 = 133^\circ C $

✔ Answer: The temperature is approximately 406 K or 133°C

> 🔥 Note: This is quite hot — a typical balloon wouldn't survive this temperature, but the calculation assumes ideal behavior.

---

✔ Final Answers Summary:

1) 9.85 moles
2) 36.06 atm
3) 274 atm
4) 243.6 moles
5) 406 K (or 133°C)

Let me know if you'd like these rounded differently or explained step-by-step further!