Detailed handwritten solutions to ideal gas law problems, including calculations and formulas.

Let’s solve each problem step by step using the Ideal Gas Law:

Ideal Gas Law Formula:
> PV = nRT

Where:
- P = pressure (in atm)
- V = volume (in liters)
- n = number of moles
- R = gas constant = 0.0821 L·atm/(mol·K)
- T = temperature (in Kelvin) — remember to convert °C to K by adding 273!

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Problem 1:

*If there is 0.5 moles of a gas at a pressure of 0.8 atm and a volume of 12 L, what is the temperature?*

We are given:
- n = 0.5 mol
- P = 0.8 atm
- V = 12 L
- R = 0.0821
- Find T

Rearrange formula:
T = PV / (nR)

Plug in numbers:
T = (0.8 × 12) / (0.5 × 0.0821)
= 9.6 / 0.04105
≈ 233.86 K

✔ Check: Units cancel correctly → atm·L / (mol · L·atm/mol·K) → K ✔️

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Problem 2:

*If there are 0.4 moles of gas at a pressure of 1.2 atm and a temperature of 300 K, how many liters does it occupy?*

Given:
- n = 0.4 mol
- P = 1.2 atm
- T = 300 K
- R = 0.0821
- Find V

Formula:
V = nRT / P

Plug in:
V = (0.4 × 0.0821 × 300) / 1.2
= (9.852) / 1.2
≈ 8.21 L

✔ Check: All units match → mol · L·atm/mol·K · K / atm → L ✔️

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Problem 3:

*If I contain 3 moles of gas in a container with a volume of 60 liters and at a temperature of 400 K, what is the pressure inside the container?*

Given:
- n = 3 mol
- V = 60 L
- T = 400 K
- R = 0.0821
- Find P

Formula:
P = nRT / V

Plug in:
P = (3 × 0.0821 × 400) / 60
= (98.52) / 60
≈ 1.642 atm

✔ Check: Units → mol · L·atm/mol·K · K / L → atm ✔️

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Problem 4:

*If I have 7.7 moles of gas at a pressure of 0.09 atm and at a temperature of 56°C, what is the volume of the container that the gas is in?*

First, convert temperature to Kelvin:
T = 56 + 273 = 329 K

Given:
- n = 7.7 mol
- P = 0.09 atm
- T = 329 K
- R = 0.0821
- Find V

Formula:
V = nRT / P

Plug in:
V = (7.7 × 0.0821 × 329) / 0.09
First calculate numerator:
7.7 × 0.0821 = 0.63217
0.63217 × 329 ≈ 207.98393

Now divide:
207.98393 / 0.09 ≈ 2310.93 L

✔ That seems large, but low pressure (0.09 atm) means gas expands a lot — makes sense.

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Problem 5:

*If I have 17 moles of gas at a temperature of 67°C, and a volume of 88.89 liters, what is the pressure of the gas?*

Convert T to Kelvin:
T = 67 + 273 = 340 K

Given:
- n = 17 mol
- V = 88.89 L
- T = 340 K
- R = 0.0821
- Find P

Formula:
P = nRT / V

Plug in:
P = (17 × 0.0821 × 340) / 88.89

Calculate numerator:
17 × 0.0821 = 1.3957
1.3957 × 340 ≈ 474.538

Divide:
474.538 / 88.89 ≈ 5.338 atm

✔ Reasonable for high moles and moderate temp/volume.

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Problem 6:

*If I have an unknown amount of gas at a pressure of 0.5 atm, a volume of 25 liters, and a temperature of 300 K, how many moles of gas do I have?*

Given:
- P = 0.5 atm
- V = 25 L
- T = 300 K
- R = 0.0821
- Find n

Formula:
n = PV / RT

Plug in:
n = (0.5 × 25) / (0.0821 × 300)
= 12.5 / 24.63
≈ 0.5075 mol

✔ Makes sense — small pressure and volume, so few moles.

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Final Answer:

1. 233.86 K
2. 8.21 L
3. 1.642 atm
4. 2310.93 L
5. 5.338 atm
6. 0.5075 mol