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Chapter 5: Problem 44

At 741 torr and \(44^{\circ} \mathrm{C}, 7.10 \mathrm{~g}\) of a gas occupy a volume of \(5.40 \mathrm{~L}\). What is the molar mass of the gas?

Short Answer

Expert verified
The molar mass of the gas is approximately 31.8 g/mol.

Step by step solution

01

Convert all quantities to SI units

First, convert the given pressure from torr to atm by using the conversion factor 1 atm = 760 torr. This gives \(P = 741 \, \text{torr} \times \frac{1 \, \text{atm}}{760 \, \text{torr}} = 0.975 \, \text{atm}\). Next, convert the temperature from Celsius to Kelvin by adding 273.15. This gives \(T = 44^{\circ} \mathrm{C} + 273.15 = 317.15 \, \mathrm{K}\). The given volume is already in liters, so no conversion is necessary.
02

Plug the values into the ideal gas law, solve for n

Replace P, V, and T in the ideal gas law equation \(PV = nRT\) with the values obtained in Step 1. Use the value of R is 0.0821 L atm/mol K. This gives \(0.975 \, \text{atm} \times 5.40 \, \text{L} = n \times 0.0821 \, \text{L atm/mol K} \times 317.15 \, \text{K}\). Solve for n to obtain \(n = \frac{0.975 \, \text{atm} \times 5.40 \, \text{L}}{0.0821 \, \text{L atm/mol K} \times 317.15 \, \text{K}}\).
03

Calculate the molar mass

The molar mass of the gas is the mass of the gas divided by the number of moles. So, \(\text{molar mass} = \frac{7.10 \, \text{g}}{n \, \text{mol}}\).

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Most popular questions from this chapter

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