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------------------------------------------------ A 1.00 g sample of an unknown gas has a pressure of 35.8 mmHg, a volume of 20.0 L, and a temperature of 25 degrees Celsius. What is the molar mass?

The molar mass of the unknown gas, calculated using the Ideal Gas Law, is found to be 312.5 g/mol when pressure, volume, and temperature are properly converted to their respective standard units.

Explanation:

To calculate the molar mass of the unknown gas given its pressure, volume, and temperature, we will use 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.

First, we need to convert pressure to atmospheres (1 atm = 760 mmHg), volume to liters if not already, temperature to Kelvin (K = °C + 273.15), and the mass to grams. The Ideal Gas Law needs all units in this standard form.

Pressure: 35.8 mmHg / 760 mmHg/atm = 0.0471 atm
Volume: already in liters (20.0 L)
Temperature: 25 °C + 273.15 = 298.15 K

The ideal gas constant (R) = 0.0821 L atm/mol K.

Next, solve for n (number of moles) using the rearranged Ideal Gas Law equation:

n = PV / RT = (0.0471 atm x 20.0 L) / (0.0821 L atm/mol K x 298.15 K) = 0.00320 mol

Finally, to find the molar mass (MM), we use the mass of the sample (m) divided by the number of moles (n):

MM = m / n = 1.00 g / 0.00320 mol = 312.5 g/mol