☰ Contents · Chemistry (General chemistry)

The Mendeleev–Clapeyron equation

Lessons 8 · 1 lessons · S. Masharipov, A. Mutalibov, E. Murodov, H. Islomova. General chemistry, Grade 11, 1st edition. G‘afur G‘ulom Publishing and Printing House, Tashkent, 2018
8

The Mendeleev–Clapeyron equation

Textbook: pp. 45–50
GoalExplain normal conditions and the Mendeleev–Clapeyron equation PV = nRT and calculate the volume, pressure, temperature, mass and molar mass of a gas under any conditions.
New words
normal conditions · normal sharoitideal gas · ideal gazuniversal gas constant · universal gaz doimiysiKelvin scale · Kelvin shkalasi
Explanation

Normal conditions: temperature 0 °C (273 K) and pressure 101.325 kPa (1 atm = 760 mmHg). Reactions do not always run under these conditions, so the ideal gas equation, the Mendeleev–Clapeyron equation, is used: PV = nRT. Here P is pressure, V volume, n the amount of substance (mol), T the temperature in kelvin and R the universal gas constant. With pressure in kPa and volume in litres R = 8.31 kPa·L/(mol·K); with pressure in atmospheres R ≈ 0.082 atm·L/(mol·K). To go from Celsius to kelvin: T = t + 273. Since n = m/M, the equation can also be written PV = (m/M)·RT, that is M = mRT/(PV), which lets you find the molar mass of a gas and identify an unknown gas. At constant temperature, doubling the pressure halves the volume; the equation also gives the right result for normal conditions: for 1 mol, V = 8.31·273/101.325 ≈ 22.4 L.

Worked examples
What volume do 2 mol of gas occupy at 27 °C and 249.3 kPa? T = 27 + 273 = 300 K; V = nRT/P = 2·8.31·300/249.3 = 20 L.
A 1 L vessel holds 1.6 g of gas at 27 °C and 124.65 kPa. M = mRT/(PV) = 1.6·8.31·300/(124.65·1) = 32 g/mol — this could be oxygen.
Class activity

Calculation workshop: for 1 mol of a gas calculate the volume under normal conditions and then at 27 °C and 100 kPa; compare and discuss how temperature and pressure affect the volume.

Practice
1
1 mol of gas occupies 24.93 L at 27 °C. What is its pressure in kPa?
2
2 mol of gas occupy 16.62 L at a pressure of 300 kPa. What is the temperature in °C?
3
What is the mass in grams of 15 L of CO₂ (M = 44 g/mol) at 83.1 kPa and 27 °C?
4
Why must the temperature in PV = nRT be taken in kelvin?