Answer :
Certainly! Let's solve the problem step-by-step.
Given:
1. Initial pressure of \( O_2 \): \( P_{ O_2} = 1.4 \) atm.
2. Total pressure after adding \( CO_2 \): \( P_{ total} = 9.7 \) atm.
Objective:
We need to find the partial pressures of \( O_2 \) and \( CO_2 \) in the final mixture. Both answers need to have the correct number of significant figures.
### Part 1 of 2
The partial pressure of \( O_2 \) remains the same as initially given because no \( O_2 \) was added or removed. Therefore, the partial pressure of \( O_2 \) is:
[tex]\[ P_{ O_2} = 1.4 \, \text{atm} \][/tex]
### Part 2 of 2
To find the partial pressure of \( CO_2 \), we subtract the initial pressure of \( O_2 \) from the total pressure:
[tex]\[ P_{ CO_2} = P_{ total} - P_{ O_2} \][/tex]
Substitute the values:
[tex]\[ P_{ CO_2} = 9.7 \, \text{atm} - 1.4 \, \text{atm} \][/tex]
Calculate the result:
[tex]\[ P_{ CO_2} = 8.3 \, \text{atm} \][/tex]
Both answers have correct significant figures:
- \( 1.4 \) atm has 2 significant figures.
- \( 9.7 \) atm has 2 significant figures.
- Therefore, the computed partial pressure of \( CO_2 \) should also be rounded to 2 significant figures (which it already is).
### Summary:
#### Part 1 of 2
[tex]\[ P_{ O_2} = 1.4 \, \text{atm} \][/tex]
#### Part 2 of 2
[tex]\[ P_{ CO_2} = 8.3 \, \text{atm} \][/tex]
Given:
1. Initial pressure of \( O_2 \): \( P_{ O_2} = 1.4 \) atm.
2. Total pressure after adding \( CO_2 \): \( P_{ total} = 9.7 \) atm.
Objective:
We need to find the partial pressures of \( O_2 \) and \( CO_2 \) in the final mixture. Both answers need to have the correct number of significant figures.
### Part 1 of 2
The partial pressure of \( O_2 \) remains the same as initially given because no \( O_2 \) was added or removed. Therefore, the partial pressure of \( O_2 \) is:
[tex]\[ P_{ O_2} = 1.4 \, \text{atm} \][/tex]
### Part 2 of 2
To find the partial pressure of \( CO_2 \), we subtract the initial pressure of \( O_2 \) from the total pressure:
[tex]\[ P_{ CO_2} = P_{ total} - P_{ O_2} \][/tex]
Substitute the values:
[tex]\[ P_{ CO_2} = 9.7 \, \text{atm} - 1.4 \, \text{atm} \][/tex]
Calculate the result:
[tex]\[ P_{ CO_2} = 8.3 \, \text{atm} \][/tex]
Both answers have correct significant figures:
- \( 1.4 \) atm has 2 significant figures.
- \( 9.7 \) atm has 2 significant figures.
- Therefore, the computed partial pressure of \( CO_2 \) should also be rounded to 2 significant figures (which it already is).
### Summary:
#### Part 1 of 2
[tex]\[ P_{ O_2} = 1.4 \, \text{atm} \][/tex]
#### Part 2 of 2
[tex]\[ P_{ CO_2} = 8.3 \, \text{atm} \][/tex]
