Calculating the Pressure of Hydrogen Gas Using the Ideal Gas Law

When dealing with gases at various conditions, the Ideal Gas Law is a powerful tool to determine the physical properties of these substances. The Ideal Gas Law can be expressed as:

PV nRT

Where:

P is the pressure of the gas, V is the volume of the gas, n is the number of moles of gas, R is the ideal gas constant, T is the temperature of the gas in Kelvin.

Step 1: Convert Temperature to Kelvin

The temperature in Celsius is given as 16°C. To convert this to Kelvin, use the following formula:

TK 16 273.15 289.15 K

Step 2: Plug in the Values into the Ideal Gas Law

Given values are:

n 0.412 moles, V 3.25 L, R 0.0821 L·atm/K·mol, T 289.15 K.

Rearrange the Ideal Gas Law to solve for pressure (P):

P (nRT) / V

Step 3: Calculate the Pressure

Substituting the values into the equation:

P (0.412 mol × 0.0821 L·atm/K·mol × 289.15 K) / 3.25 L

Calculating the numerator:

0.412 × 0.0821 × 289.15 ≈ 9.768 L·atm

Divide by the volume:

P ≈ 9.768 L·atm / 3.25 L ≈ 3.00 atm

Conclusion

The pressure of the hydrogen gas is approximately 3.00 atm.

Alternative Methods

For those interested in practicing with different applications, solving the same problem with the Van der Waal’s equation could provide a slightly different result due to the approximation of real gases. However, for the given conditions, the ideal gas law yields a reliable result.

Another method uses a different value of the ideal gas constant:

P (0.412 mol × 0.08314 L·kPa/mol·K × 289 K) / 3.25 L 304 kPa

This method yields a pressure in kPa, suggesting that the constant R should be chosen to match the desired units.

Summary

The Ideal Gas Law is a fundamental concept in chemistry and physics. Users can easily calculate the pressure of a gas given its temperature, volume, and number of moles by following a few straightforward steps. Understanding and being able to apply this law is crucial for solving various problems in the field.

Additional Resources

For further reading and practice, consider exploring online calculators and physics textbooks that provide detailed explanations and examples.