An experiment shows that a 245mL gas sample has a mass of 0.436g at a pressure of 757 mmHg and a temperature of 29C.
What is the molar mass of the gas?

Question

An experiment shows that a 245mL gas sample has a mass of 0.436g  at a pressure of 757 mmHg and a temperature of 29C.
What is the molar mass of the gas?

Naomi Aronson · Accepted Answer

#"44.3 g/mol"#

The idea behind this is that in order to calculate the number of moles of gas in that sample, you must apply the equation for the ideal gas law.

You can solve for the gas's molar mass once you know how many moles of that particular mass there are.

Thus, this is how the ideal gas law equation appears.

#color(blue)(PV = nRT)" "#, where

#P# - the pressure of the gas #V# - the volume it occupies #n# - the number of moles of gas #R# - the universal gas constant, usually given as #0.082("atm" * "L")/("mol" * "K")# #T# - the temperature of the gas, expressed in Kelvin

Now, it's crucial to note that the pressure, temperature, and volume values provided to you do not use the units specified by the universal gas constant.

This implies that prior to entering the values into the ideal gas law equation, you will need to perform a few conversions. Specifically, you must have

With this in mind, rearrange the ideal gas law equation and solve for #n#

#PV = nRT implies n = (PV)/(RT)#

#n = (757/760color(red)(cancel(color(black)("atm"))) * 245 * 10^(-3)color(red)(cancel(color(black)("L"))))/(0.082(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 29)color(red)(cancel(color(black)("K"))))#

#n = "0.00985 moles"#

Molar mass is now understood to be mass per mole.

#color(blue)("molar mass" = "mass"/"no. of moles")#

In your instance, the sample's molar mass will be

#M_"M" = m/n#

#M_"M" = "0.436 g"/"0.00985 moles" = "44.264 g/mol"#

Even though you only have two sig figs for the temperature, I'll leave this rounded to three sig figs for now.

#M_"M" = color(green)("44.3 g/mol")#

Jose Ayala · Answer

undefined The molar mass of the gas can be calculated using 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 temperature to Kelvin:

$ P = 757 \, \text{mmHg} \times \frac{1 \, \text{atm}}{760 \, \text{mmHg}} = 0.996 \, \text{atm} $

$ T = 29^\circ C + 273.15 = 302.15 \, \text{K} $

Next, we need to calculate the number of moles of the gas using the formula:

$ n = \frac{m}{M} $, where $ m $ is the mass of the gas and $ M $ is the molar mass.

$ m = 0.436 \, \text{g} $

$ n = \frac{0.436 \, \text{g}}{M} $

Now, we can rearrange the ideal gas law equation to solve for $ M $:

$ M = \frac{m}{n} $

Substitute the known values:

$ M = \frac{0.436 \, \text{g}}{\frac{PV}{RT}} $

$ M = \frac{0.436 \, \text{g} \times RT}{PV} $

$ M = \frac{0.436 \, \text{g} \times (0.0821 \, \text{atm} \cdot \text{L} / \text{mol} \cdot \text{K}) \times 302.15 \, \text{K}}{0.996 \, \text{atm} \times 0.245 \, \text{L}} $

$ M \approx \frac{0.436 \times 24.83}{0.996 \times 0.245} $

$ M \approx \frac{10.828}{0.24462} $

$ M \approx 44.28 \, \text{g/mol} $

Therefore, the molar mass of the gas is approximately $ 44.28 \, \text{g/mol} $.

An experiment shows that a 245mL gas sample has a mass of 0.436g at a pressure of 757 mmHg and a temperature of 29C. What is the molar mass of the gas?