Problem 87 - Chemistry and Chemical Reactivity

Question

Argon is present in dry air to the extent of \(0.93 \%\) by volume. What quantity of argon is present in \(1.00 \mathrm{L}\) of air? If you wanted to isolate 1.00 mol of argon, what volume of air would you need at 1.00 atm pressure and \(25^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

1.00 mole of argon requires about 2624 L of air.

Step 1: Calculate Volume of Argon in 1.00 L Air

Determine how much argon is present in 1.00 L of air. Given that argon constitutes \(0.93\%\) of the air by volume, calculate the argon volume: \(0.0093 \times 1.00 \ \text{L} = 0.0093 \ \text{L}.\) This means there are \(0.0093\) liters of argon in \(1.00\) liter of air.

Step 2: Convert Conditions to Moles Using Ideal Gas Law

Use the ideal gas law, \(PV = nRT\), to find how many moles are in 0.0093 liters of argon at 1.00 atm and \(25^{\circ} \mathrm{C}\). First, convert the temperature to Kelvin: \(25 + 273.15 = 298.15 \ \text{K}\). Use \(R = 0.0821 \ \text{L atm/mol K}\) and solve for \(n\):\[ n = \frac{PV}{RT} = \frac{1.00 \times 0.0093}{0.0821 \times 298.15} \approx 0.000381 \ \text{mol}. \]

Step 3: Calculate Volume of Air Needed for 1.00 mol Argon

Determine the volume of air needed to isolate 1.00 mol of argon. Since \(0.0093\) liters of air gives \(0.000381\) mol of argon, use proportions:\[ \frac{1.00 \ \text{mol}}{0.000381 \ \text{mol/L}} = x \ \text{L of air}, \]where \(x\) is the volume of air needed. Solving for \(x\) gives:\[ x \approx \frac{1.00}{0.000381} \approx 2624 \ \text{L}. \]

Step 4: Conclusion

To isolate 1.00 mole of argon, you need approximately \(2624\) liters of air at 1.00 atm pressure and \(25^{\circ} \mathrm{C}\).

Key Concepts

Mole concept

The mole concept is a fundamental idea in chemistry that allows us to count particles at the atomic level. A mole ( ) is a unit used to measure the amount of substance and is defined as exactly 6.022 x 10^{23} particles, which can be atoms, molecules, or ions. This number is known as Avogadro's Number.
Understanding moles is crucial when dealing with gases like argon because it connects macroscopic quantities with atomic-scale interactions. With the Ideal Gas Law, we can convert between volume, temperature, pressure, and moles of a gas. When calculating reactions or isolating gases in chemistry, expressing quantities in moles makes it easier to compare and analyze different substances.
Using the Ideal Gas Law as part of the mole concept, we can determine how much substance is present under given conditions or predict the conditions needed to achieve a specific quantity.

Argon gas

Argon is a noble gas, meaning it is inert and does not react easily with other elements. It is a colorless and tasteless gas that you can find in the air; in fact, it makes up about 0.93% of the earth's atmosphere by volume. Even though it is a small percentage, it's still significant given the vast volume of Earth's atmosphere. Argon's properties make it incredibly useful in various industries. For example, it is used in lighting because it does not react with the filament, and in welding, it provides an inert atmosphere that prevents oxidation. Because it is a gas at room temperature, understanding how it behaves under different conditions is important for its practical applications.
When calculating how much argon is present in a given volume of air, or determining the volume of air needed to extract a specific amount of argon, it is crucial to know its proportion in the atmosphere and apply principles like the Ideal Gas Law.

Volume of gas calculations

Volume of gas calculations play an essential role when working with gases. To accurately determine the volume of gas, or relate volume to other properties, such as pressure or temperature, we use the Ideal Gas Law, which is expressed as:\[ PV = nRT \] Here,

• \( P \) is the pressure of the gas.




• \( V \) is the volume occupied by the gas.




• \( n \) is the amount of gas in moles.




• \( R \) is the universal gas constant.




• \( T \) is the temperature of the gas in Kelvin.

In the exercise, we used this formula to calculate the moles of argon in a given volume of air. Once you have the amount in moles, you can use ratio calculations to determine how much volume of air is needed to gather a specific amount of argon. This technique simplifies the understanding of gas volumes within closed systems, making it an invaluable tool in both laboratory settings and industrial applications.