How many moles of chlorine gas at 120. °C and 33.3 atm would occupy a vessel of 40.0 L?

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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**Problem:**

*Question 7 of 14*

How many moles of chlorine gas at 120. °C and 33.3 atm would occupy a vessel of 40.0 L?

**Answer:**

0.807 mol

**Explanation:**

This is a chemistry problem requiring the use of the ideal gas law equation:

\[ PV = nRT \]

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

**Calculation Steps:**

1. Convert the temperature from Celsius to Kelvin:
   \[ T(K) = 120 + 273.15 = 393.15 \, K \]

2. Rearrange the ideal gas law to solve for the number of moles (\( n \)):
   \[ n = \frac{PV}{RT} \]

3. Insert the known values into the equation:
   \[ n = \frac{(33.3 \, \text{atm})(40.0 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K})(393.15 \, \text{K})} \]

4. Calculate the number of moles:
   \[ n \approx 0.807 \, \text{mol} \]

This calculation gives the number of moles of chlorine gas under the specified conditions.
Transcribed Image Text:**Problem:** *Question 7 of 14* How many moles of chlorine gas at 120. °C and 33.3 atm would occupy a vessel of 40.0 L? **Answer:** 0.807 mol **Explanation:** This is a chemistry problem requiring the use of the ideal gas law equation: \[ PV = nRT \] Where: - \( P \) = pressure in atmospheres (atm) - \( V \) = volume in liters (L) - \( n \) = number of moles - \( R \) = ideal gas constant (0.0821 L·atm/mol·K) - \( T \) = temperature in Kelvin (K) **Calculation Steps:** 1. Convert the temperature from Celsius to Kelvin: \[ T(K) = 120 + 273.15 = 393.15 \, K \] 2. Rearrange the ideal gas law to solve for the number of moles (\( n \)): \[ n = \frac{PV}{RT} \] 3. Insert the known values into the equation: \[ n = \frac{(33.3 \, \text{atm})(40.0 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K})(393.15 \, \text{K})} \] 4. Calculate the number of moles: \[ n \approx 0.807 \, \text{mol} \] This calculation gives the number of moles of chlorine gas under the specified conditions.
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