Question

What is the molar mass of a gas if 0.281 g of the gas occupies a volume of 125 ml at a temperature 126 °c and a pressure of 777 torr?

Answer 1

To find the molar mass of a gas given its mass, volume, temperature, and pressure, convert all measurements to their proper units and use the ideal gas law equation. After calculating the number of moles, divide the mass of the gas by the number of moles to get the molar mass.

Step-by-step explanation:

The molar mass of a gas can be computed using the ideal gas law equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. In this case, the volume needs to be converted to liters and the temperature to Kelvin. Also, the pressure in torr must be converted to atmospheres (1 atm = 760 torr).

First, convert the temperature to Kelvin: T = 126 + 273 = 399 K. Convert the volume to liters: V = 125 mL = 0.125 L. Convert the pressure to atm: P = 777 torr * (1 atm / 760 torr) = 1.022 atm.

Next, solve for n (number of moles) using the rearranged ideal gas law: n = PV / RT. Finally, calculate the molar mass (M) by dividing the mass of the gas (m) by the number of moles (n): M = m / n.

Using the values P = 1.022 atm, V = 0.125 L, R = 0.0821 atm·L/mol·K (ideal gas constant), and T = 399 K, the calculation will yield the molar mass of the gas.

Answer 2

Answer : 72.05 g/mol

Explanation :

Let's assume that the given gas is an ideal gas. Then we can use ideal gas equation,
PV = nRT

Where,
P = Pressure of the gas (Pa)
V = volume of the gas (m³)
n = number of moles (mol)
R = Universal gas constant (8.314 J mol⁻¹ K⁻¹)
T = temperature in Kelvin (K)

The given data for the gas is,
P = 777 torr = 103591 Pa
V = 125 mL = 125 x 10⁻⁶ m³
T = (126 + 273) = 399 K
R = 8.314 J mol⁻¹ K⁻¹
n = ?

By applying the formula,
103591 Pa x 125 x 10⁻⁶ m³ = n x 8.314 J mol⁻¹ K⁻¹ x 399 K
n = 3.90 x 10⁻³ mol

Moles (mol) = mass (g) / molar mass (g/mol)

Mass of the gas = 0.281 g
Moles of the gas = 3.90 x 10⁻³ mol
Hence,
molar mass of the gas = mass / moles
= 0.281 g / 3.90 x 10⁻³ mol
= 72.05 g/mol