A 4.00 L rigid container holds 0.250 mol of nitrogen gas at a pressure of 1.50 atm. What is the temperature of the gas in degrees Celsius? (R = 0.0821 L·atm·mol⁻¹·K⁻¹)

Correct answer

A. 19.2 °C

Principle or equation

The ideal gas equation is PV = nRT, where P is pressure, V is volume, n is amount of substance, R is the gas constant, and T is absolute temperature in kelvin. Temperature in Celsius is obtained by subtracting 273.15 from the kelvin value.

Why this answer is correct

Rearrange the ideal gas equation to solve for T: T = PV / (nR). Substitute the given values: P = 1.50 atm, V = 4.00 L, n = 0.250 mol, R = 0.0821 L·atm·mol⁻¹·K⁻¹. T = (1.50 × 4.00) / (0.250 × 0.0821) = 6.00 / 0.020525 ≈ 292.3 K. Convert to Celsius: 292.3 - 273.15 ≈ 19.2 °C.

Example

For 0.500 mol of gas at 2.00 atm in a 10.0 L container: T = (2.00 × 10.0) / (0.500 × 0.0821) ≈ 487 K = 214 °C.