\(
PV = nRT \)
STRICT SI UNIT RULE
You MUST convert to these units before calculating, or your answer will be wrong by a factor of 1000.
Pressure (P)
Pa
If kPa → ×1000
Volume (V)
m³
If dm³ → ÷1000
If cm³ → ÷1,000,000
Temp (T)
K
If °C → +273
Gas Phase Calculation
Problem: Calculate the number of moles of gas in a 2.0 dm³ cylinder at 100 kPa and 27°C.
1. Convert Units (CRITICAL STEP):
- V: 2.0 dm³ = \( 2.0 \div 1000 = 0.002 \text{ m}^3 \)
- P: 100 kPa = \( 100 \times 1000 = 100{,}000 \text{ Pa} \)
- T: 27°C = \( 27 + 273 = 300 \text{ K} \)
2. Rearrange Formula to find n:
\( n = \frac{PV}{RT} \)
3. Substitute & Solve:
\( n = \frac{100{,}000 \times 0.002}{8.31 \times 300} \)
\( n = 0.080 \text{ mol} \)