Question

Determine the molar mass of a 0.643-g sample of gas occupies 125 mL at 60. cm of Hg and 25°C

Answer 1

To determine the molar mass of the gas, we need to use the ideal gas law, 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. We can rearrange this equation to solve for n:

n = PV/RT

First, we need to convert the pressure to atmospheres (atm) and the volume to liters (L):

cm Hg = 0.788 atm (using the conversion factor 1 atm = 760 mm Hg)

125 mL = 0.125 L

Next, we can substitute the given values into the equation and solve for n:

n = (0.788 atm)(0.125 L)/(0.0821 L·atm/mol·K)(298 K) = 0.00472 mol

Finally, we can calculate the molar mass by dividing the mass of the sample by the number of moles:

molar mass = 0.643 g/0.00472 mol = 136 g/mol (rounded to three significant figures)

Therefore, the molar mass of the gas is approximately 136 g/mol.

Answer 2

Step-by-step explanation:

To determine the molar mass of the gas, we need to use the ideal gas law equation:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for the number of moles:

n = (PV) / (RT)

We are given the mass of the gas (0.643 g), the volume (125 mL), the pressure (60. cm Hg), and the temperature (25°C). To use these values in the ideal gas law equation, we need to convert the volume to liters and the pressure to atmospheres (atm) and the temperature to Kelvin (K):

V = 125 mL = 0.125 L

P = 60. cm Hg = 0.789 atm (using the conversion factor 1 atm = 760 mm Hg and 1 cm Hg = 1.33322 mm Hg)

T = 25°C + 273.15 = 298.15 K

Substituting these values into the ideal gas law equation and solving for n gives:

n = (PV) / (RT) = (0.789 atm x 0.125 L) / (0.0821 L·atm/mol·K x 298.15 K) = 0.00314 mol

To find the molar mass, we can use the formula:

molar mass = mass of sample / number of moles

molar mass = 0.643 g / 0.00314 mol = 204.46 g/mol

Therefore, the molar mass of the gas is approximately 204.46 g/mol.