Calculation of Molar Mass of Gas

To determine the molar mass of a gas given its mass and volume at NTP, the following steps can be followed:

Step 1: Convert the volume of the gas from cm³ to m³.

- 1 cm³ = 1 x 10^-6 m³
- Therefore, 112 cm³ = 112 x 10^-6 m³ = 0.000112 m³

Step 2: Convert the temperature and pressure to their SI units.

- NTP refers to Normal Temperature and Pressure, which is defined as 0°C (273 K) and 1 atm (101.325 kPa) respectively.
- Therefore, the temperature in SI units is 273 K and the pressure is 101.325 kPa.

Step 3: Use the ideal gas law to calculate the number of moles of gas.

- The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
- Rearranging the formula to solve for n, we get n = PV/RT.
- Substituting the values given, we get n = (101.325 kPa)(0.000112 m³)/(8.314 J/mol.K)(273 K) = 0.00000411 mol

Step 4: Calculate the molar mass of the gas.

- The molar mass is the mass of one mole of the gas.
- It can be calculated by dividing the mass of the gas by the number of moles, which we calculated in Step 3.
- Since the mass of the gas is given as 0.56 g, we get molar mass = 0.56 g/0.00000411 mol = 136.02 g/mol.

Therefore, the molar mass of the gas is 136.02 g/mol.

Correct answer is 112 gm/molWe have number of moles=given mass/molar mass=volume (in litres)/22.4 (for gases at NTP or STP) So, 0.56/M=(112x10^(-3))/22.4Therefore, M=(0.56x22.4)/0.112=112