Question

To identify a diatomic gas ( X₂), a researcher carried out the following experiment: she weighed an empty 2.0- l bulb, then filled it with the gas at 1.50 atm and 25.0 ∘c and weighed it again. the difference in mass was 3.5 g . identify the gas.

Answer 1

To identify the diatomic gas, we first calculated the molar mass using the ideal gas equation and then identified the gas as oxygen (O₂) because the calculated molar mass matched the known molar mass of oxygen.

Step-by-step explanation:

To identify a diatomic gas (X₂), we can use the ideal gas equation to calculate the molar mass of the gas and then compare it to known gases. Given that the volume of the gas is 2.0 liters, the pressure is 1.50 atm, and the temperature is 25.0 °C (which converts to 298.15 K), and the increase in mass is 3.5 grams, we can calculate the molar mass of the gas using the ideal gas law PV = nRT, where n is the number of moles and R is the ideal gas constant (0.0821 L·atm/K·mol).

First convert the mass to moles (n = mass/molar mass), then solve for the molar mass (MM). We know:
P = 1.50 atm,
V = 2.0 L,
n = 3.5 g / MM,
T = 298.15 K,
R = 0.0821 L·atm/K·mol.

Substituting the known values into PV = nRT, we get:
1.50 atm × 2.0 L = (3.5 g / MM) × 0.0821 L·atm/K·mol × 298.15 K.
After rearranging and solving for MM, we get:
MM = (3.5 g × 0.0821 L·atm/K·mol × 298.15 K) / (1.50 atm × 2.0 L) = 31.9988 g/mol.

Comparing this calculated molar mass with molar masses of known diatomic gases, we identify the gas as oxygen (O₂) because the molar mass of O₂ is approximately 32 g/mol, which matches our calculated value.