Question

A 1.15 g sample of an unknown gas at 63 ∘C and 1.10 atm is stored in a 2.75 L flask.

What is the molar mass of the gas? What is the density of the gas?

Answer 1

To calculate the molar mass of the unknown gas, we can use the ideal gas law equation PV = nRT. Then, we can calculate the density of the gas using the formula density = mass / volume.

Step-by-step explanation:

To calculate the molar mass of the unknown gas, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

First, we need to convert the given pressure to atm and the given volume to liters. The pressure is already in atm, so no conversion is needed. To convert the volume from mL to L, divide it by 1000.

Next, we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = (PV) / (RT)

Plugging in the given values and the ideal gas constant (0.0821 L•atm/mol•K), we can calculate the number of moles. Finally, we can divide the mass of the unknown gas sample (1.15 g) by the number of moles to find the molar mass.

To calculate the density of the gas, we can use the formula density = mass / volume. Plugging in the given values, we can calculate the density of the gas.

Answer 2

The molar mass of the gas is calculated to be 96.64 g/mol and the density of the gas is determined to be 0.418 g/L using the ideal gas law and basic density formula.

Step-by-step explanation:

The molar mass of an unknown gas can be found using the ideal gas law, which is PV = nRT. Given: the mass of the gas (1.15 g), temperature (63 ℃), pressure (1.10 atm), and volume (2.75 L). First, convert the temperature to Kelvin (T = 63 ℃ + 273 = 336 K). Using the ideal gas law rearranged to solve for n (n = PV/RT), substitute the known values and the value of R (0.0821 L·atm/K·mol) to calculate the number of moles.

n = (1.10 atm × 2.75 L) / (0.0821 L·atm/K·mol × 336 K) = 0.0119 mol. The molar mass (MM) is then mass/n, so MM = 1.15 g / 0.0119 mol = 96.64 g/mol.

To calculate the density of the gas, use the formula density = mass/volume. Density = 1.15 g / 2.75 L = 0.418 g/L.