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Chapter 10: Problem 108

An 8.40 -g sample of argon and an unknown mass of \(\mathrm{H}_{2}\) are mixed in a flask at room temperature. The partial pressure of the argon is $44.0 \mathrm{kPa},\( and that of the hydrogen is \)57.33 \mathrm{kPa} .$ What is the mass of the hydrogen?

Short Answer

Expert verified
First, we find the number of moles of argon gas by dividing its mass (8.40 g) by its molar mass (39.95 g/mol). Then, using the Ideal Gas Law, we find the volume of the container, given the partial pressure of argon (44 kPa) and assuming a room temperature of 298 K. Next, we calculate the number of moles of hydrogen gas using the Ideal Gas Law again, this time with the partial pressure of hydrogen (57.33 kPa). Finally, we find the mass of hydrogen gas by multiplying the number of moles of hydrogen by its molar mass (2.02 g/mol). After performing the calculations, we obtain the mass of the hydrogen gas in the mixture.

Step by step solution

01

Find the number of moles of argon gas in the mixture.

To find the number of moles of the argon gas, we can use the following formula: Number of moles = Mass of the gas / Molar mass of the gas The molar mass of argon gas is \(39.95 \mathrm{g/mol}\). Given the mass of argon gas (8.40 grams), we can now find the number of moles: Number of moles of argon = \(8.40 \mathrm{g} / 39.95 \mathrm{g/mol}\) Calculate the number of moles of argon gas.
02

Use the Ideal Gas Law to find the volume of the container.

Since we know the pressure and the number of moles of argon gas, we can now find the volume of the container. The Ideal Gas Law equation can be written as: \(PV = nRT\) Where: P = Partial pressure of argon = \(44.0 \mathrm{kPa}\) V = Volume of the container n = Number of moles of argon R = Gas constant = \(8.314 \mathrm{J/(mol·K)}\) (Note that we need to convert the pressure in kPa to Pa) T = Room temperature (Assuming 298 K) Rearrange the equation to find the volume V: \(V = \frac{nRT}{P}\) Plug in the values and calculate the volume of the container.
03

Calculate the number of moles of hydrogen gas.

Now that we know the volume of the container, we can find the number of moles of hydrogen gas using the Ideal Gas Law formula: \(PV = nRT\) Where: P = Partial pressure of hydrogen = \(57.33 \mathrm{kPa}\) V = Volume of the container (calculated in step 2) n = Number of moles of hydrogen R = Gas constant = \(8.314 \mathrm{J/(mol·K)}\) (Note that we need to convert the pressure in kPa to Pa) T = Room temperature (298 K) Rearrange the equation to find the number of moles of hydrogen (n): \(n = \frac{PV}{RT}\) Plug in the values and calculate the number of moles of hydrogen gas.
04

Calculate the mass of hydrogen gas.

Now that we have the number of moles of hydrogen gas, we can calculate its mass using the following formula: Mass of the gas = Number of moles of the gas × Molar mass of the gas The molar mass of hydrogen gas is \(2.02 \mathrm{g/mol}\). Multiply the number of moles calculated in step 3 by the molar mass of hydrogen gas: Mass of hydrogen = (Number of moles of hydrogen) × (2.02 g/mol) Calculate the mass of the hydrogen gas. This is the answer to the exercise.

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Most popular questions from this chapter

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