Calculate the amount in moles of a gas which occupies 10.5 dm3 at 6 atm and 30oC [R = 0.082 atm dm3 K-1 $mol^{-1}$]

Analyze the question: We are given the volume, pressure and temperature of a gas and asked for the number of moles. This is an ideal gas law problem.

Concept: The ideal gas equation is

PV = nRT, so n = PV / RT

Temperature must be in Kelvin: T = 30 + 273 = 303 K

Solution:

• P = 6 atm
• V = 10.5 dm³
• R = 0.082 atm dm³ K⁻¹ mol⁻¹
• T = 303 K

n = (6 × 10.5) / (0.082 × 303)

Numerator: 6 × 10.5 = 63

Denominator: 0.082 × 303 = 24.846

n = 63 / 24.846 ≈ 2.536 mol

Answer: The calculation gives 2.

Tip: Always convert °C to K first by adding 273. Also check that your units match R's units (atm, dm³, K). If the options include a value like 0.394, that is the inverse (RT/PV), a common mistake from flipping the formula. Remember: n = PV/RT, with n on top of nothing, just "PV over RT".