Question

A sample of gas has a volume of \(3.91 \mathrm{~L}\), a temperature of \(305 \mathrm{~K}\), and a pressure of 2.09 atm. How many moles of gas are present?

Short answer

There are approximately 0.326 moles of gas.

Step-by-step solution

Identify Given Variables

You're given the following values in the problem:- Volume, \( V = 3.91 \) L- Temperature, \( T = 305 \) K- Pressure, \( P = 2.09 \) atm.

Recall the Ideal Gas Law

The Ideal Gas Law is given by the formula:\[ PV = nRT \]where:- \( P \) is the pressure,- \( V \) is the volume,- \( n \) is the number of moles,- \( R \) is the ideal gas constant (0.0821 L atm/mol K),- \( T \) is the temperature.

Rearrange the Formula

Rearrange the Ideal Gas Law formula to solve for \( n \) (the number of moles):\[ n = \frac{PV}{RT} \]

Substitute the Given Values

Substitute the given values into the rearranged formula:\[ n = \frac{(2.09 \text{ atm}) \times (3.91 \text{ L})}{(0.0821 \text{ L atm/mol K}) \times (305 \text{ K})} \]

Calculate the Result

Perform the calculation for the number of moles:\[ n = \frac{2.09 \times 3.91}{0.0821 \times 305} \approx 0.326 \] moles.

Key concepts

Moles of Gas Calculation

When working with gases, understanding how to calculate the number of moles present is crucial. The number of moles, represented as \( n \), is a central component in the Ideal Gas Law equation. In the case of our exercise, we needed to find \( n \) for a gas sample with given values of pressure, volume, and temperature.

First, ensure you have the gas parameters: pressure (\( P \)), volume (\( V \)), and temperature (\( T \)). These values will be substituted into the rearranged Ideal Gas Law equation. Remember that the result of your calculation gives you the moles of gas contained in the specific conditions provided. The unit for moles in this context is simply "mol."

For our sample calculation, substituting the values into the equation \( n = \frac{PV}{RT} \) gave us 0.326 moles. This means under these specific conditions, about 0.326 moles of gas were found in the sample. Understanding this calculation helps determine how much of a substance is present in a system.

Gas Law Constants

The Ideal Gas Law is a versatile tool in chemical calculations, and the gas law constant \( R \) plays a vital role in this equation. The constant \( R \) is used to connect the other variables in the law: pressure, volume, and temperature, with the amount of gas, or moles. Its value is typically 0.0821 L atm/mol K, suitable for many general calculations.

The choice of constant depends on the units used for pressure and volume in your problem. It's essential for students to use the correct constant version to maintain consistency across the units. In most chemistry courses, students will often use atmospheric pressure (atm) and volume in liters (L), which aligns with the 0.0821 L atm/mol K value.

• Make sure you match units across your calculation.
• Verify that \( R \) is suitable for all unit combinations used.

By using \( R \) correctly, calculations become more straightforward, and the Ideal Gas Law can accurately predict the behavior of gases under different conditions.

Rearranging Equations

Solving for a specific variable is a fundamental skill when dealing with equations. The Ideal Gas Law equation, \( PV = nRT \), can be rearranged depending on which variable you need to find. Rearranging involves solving the equation for the unknown variable by isolating it on one side.

For instance, when we need to find the number of moles \( n \), the equation is rearranged to \( n = \frac{PV}{RT} \). This step-by-step rearrangement is critical because it properly guides us on what operations to perform to isolate the variable of interest. Keeping track of units and operations during this step ensures accuracy.

Here are some tips for rearranging equations successfully:

• Identify the variable you need to solve for.
• Use algebraic operations carefully to isolate this variable.
• Double-check units to confirm they align after rearrangement.

Rearranging equations is not just a skill for gas laws but is useful across all areas of science and algebra, allowing for adaptability and precision in problem-solving.