Chemistry
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ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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![**Total Pressure Calculation of a Gas Mixture**
**Problem:**
What is the total pressure, in millimeters of mercury, of a gas mixture containing argon gas at 0.23 atm, helium gas at 290 mmHg, and nitrogen gas at 390 torr?
**Instructions:**
Express your answer using two significant figures.
**Calculation Box:**
\[ P_{\text{total}} = \boxed{} \] mmHg
---
**Explanation:**
To solve this problem, you need to sum the partial pressures of the individual gases in the same unit (mmHg). Here are the pressures of the gases listed in different units:
- Argon: 0.23 atm
- Helium: 290 mmHg
- Nitrogen: 390 torr
Note that 1 atm = 760 mmHg and 1 torr = 1 mmHg.
First, convert the pressure of argon gas from atm to mmHg:
\[ 0.23 \text{ atm} \times 760 \text{ mmHg/atm} = 174.8 \text{ mmHg} \]
Now, add all the pressures together:
\[ P_{\text{total}} = 174.8 \text{ mmHg} + 290 \text{ mmHg} + 390 \text{ mmHg} \]
\[ P_{\text{total}} = 854.8 \text{ mmHg} \]
Rounded to two significant figures, the total pressure is:
\[ P_{\text{total}} \approx 850 \text{ mmHg} \]
**Summary:**
The total pressure of the gas mixture is approximately 850 mmHg when expressed using two significant figures.](https://content.bartleby.com/qna-images/question/d7218640-a774-45e5-abf7-0db0957362b6/61549f3a-c0fc-4039-ad63-b82736f3f417/c31e38l.jpeg)
Transcribed Image Text:**Total Pressure Calculation of a Gas Mixture**
**Problem:**
What is the total pressure, in millimeters of mercury, of a gas mixture containing argon gas at 0.23 atm, helium gas at 290 mmHg, and nitrogen gas at 390 torr?
**Instructions:**
Express your answer using two significant figures.
**Calculation Box:**
\[ P_{\text{total}} = \boxed{} \] mmHg
---
**Explanation:**
To solve this problem, you need to sum the partial pressures of the individual gases in the same unit (mmHg). Here are the pressures of the gases listed in different units:
- Argon: 0.23 atm
- Helium: 290 mmHg
- Nitrogen: 390 torr
Note that 1 atm = 760 mmHg and 1 torr = 1 mmHg.
First, convert the pressure of argon gas from atm to mmHg:
\[ 0.23 \text{ atm} \times 760 \text{ mmHg/atm} = 174.8 \text{ mmHg} \]
Now, add all the pressures together:
\[ P_{\text{total}} = 174.8 \text{ mmHg} + 290 \text{ mmHg} + 390 \text{ mmHg} \]
\[ P_{\text{total}} = 854.8 \text{ mmHg} \]
Rounded to two significant figures, the total pressure is:
\[ P_{\text{total}} \approx 850 \text{ mmHg} \]
**Summary:**
The total pressure of the gas mixture is approximately 850 mmHg when expressed using two significant figures.
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