Use the ideal gas law to calculate an unknown property. A sample of O₂ gas has a volume of 811 mL, has a pressure of 541 mm Hg, and is at a temperature of 13.6 °C. Calculate the amount (in moles) of O₂ in the gas sample. mol

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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**Using the Ideal Gas Law to Determine an Unknown Property**

In this exercise, we will apply the ideal gas law to calculate an unknown property of a gas sample.

**Problem Statement:**

A sample of O₂ gas has the following properties:
- Volume: 811 mL
- Pressure: 541 mm Hg
- Temperature: 13.6 °C

**Objective:** Calculate the amount (in moles) of O₂ in the gas sample.

**Solution:**

To solve this problem, use the ideal gas law equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure in atm
- \( V \) = volume in liters
- \( n \) = number of moles
- \( R \) = ideal gas constant (0.0821 L·atm/mol·K)
- \( T \) = temperature in Kelvin

Make sure to convert the given values to the appropriate units:

1. Convert the volume from mL to L.
2. Convert the pressure from mm Hg to atm.
3. Convert the temperature from °C to Kelvin.

Finally, use the rearranged ideal gas law formula to find \( n \):

\[ n = \frac{PV}{RT} \] 

Enter your answer in the provided box in moles.
Transcribed Image Text:**Using the Ideal Gas Law to Determine an Unknown Property** In this exercise, we will apply the ideal gas law to calculate an unknown property of a gas sample. **Problem Statement:** A sample of O₂ gas has the following properties: - Volume: 811 mL - Pressure: 541 mm Hg - Temperature: 13.6 °C **Objective:** Calculate the amount (in moles) of O₂ in the gas sample. **Solution:** To solve this problem, use the ideal gas law equation: \[ PV = nRT \] Where: - \( P \) = pressure in atm - \( V \) = volume in liters - \( n \) = number of moles - \( R \) = ideal gas constant (0.0821 L·atm/mol·K) - \( T \) = temperature in Kelvin Make sure to convert the given values to the appropriate units: 1. Convert the volume from mL to L. 2. Convert the pressure from mm Hg to atm. 3. Convert the temperature from °C to Kelvin. Finally, use the rearranged ideal gas law formula to find \( n \): \[ n = \frac{PV}{RT} \] Enter your answer in the provided box in moles.
Expert Solution
Step 1

Given -

Volume of O2 =811 mL = 0.811 L 

(1L = 1000ml)

Pressure of O2= 41 mmHg 

Temperature =13.6 °C = 13.6 + 273 = 286.6 K

 

 

 

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