The density of a certain gas is 1.98gdm-3 at s.t.p. What is the molecular mas of the gas?

The density of a certain gas is 1.98gdm-3 at s.t.p. What is the molecular mas of the gas?

Answer Details

The molecular mass of the gas can be determined using the ideal gas equation, which relates the density, molecular mass, pressure, and temperature of a gas. At standard temperature and pressure (STP), the pressure is 1 atm and the temperature is 273 K. The ideal gas equation can be written as: PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. At STP, the volume of one mole of gas is 22.4 L. Therefore, the number of moles of the gas can be calculated as: n = V/22.4 where V is the volume of the gas. The density of the gas is given as 1.98 g/dm^3. Converting this to g/L, we get: 1.98 g/dm^3 x (1 dm/10 cm)^3 = 1.98 g/L Substituting the values into the ideal gas equation, we get: (1 atm) (V) = (n) (0.0821 L atm/mol K) (273 K) Solving for n, we get: n = (1 atm) (V) / (0.0821 L atm/mol K) (273 K) Substituting n = V/22.4, we get: V/22.4 = (1 atm) (V) / (0.0821 L atm/mol K) (273 K) Solving for V, we get: V = (22.4 L) (0.0821 L atm/mol K) (273 K) / (1 atm) = 22.4 L Therefore, the number of moles of the gas is: n = V/22.4 = 22.4 L / 22.4 L/mol = 1 mol The molecular mass of the gas can be calculated using the formula: molecular mass = mass / number of moles The mass of the gas is the density multiplied by the volume occupied by one mole of the gas, which is 22.4 L at STP. Therefore, the mass of the gas is: mass = density x volume = 1.98 g/L x 22.4 L/mol = 44.35 g/mol Thus, the molecular mass of the gas is approximately 44.0 g/mol, which is the first option.