Answer :
To find the total pressure of the gas mixture, you need to add up the partial pressures of each individual gas present in the mixture. This is done using Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.
Given the partial pressures:
- Oxygen (\(O_2\)): \(0.875 \, \text{atm}\)
- Nitrogen (\(N_2\)): \(0.0553 \, \text{atm}\)
- Argon (\(Ar\)): \(0.00652 \, \text{atm}\)
Step-by-step solution:
1. Identify the partial pressures:
- \( P_{O_2} = 0.875 \, \text{atm} \)
- \( P_{N_2} = 0.0553 \, \text{atm} \)
- \( P_{Ar} = 0.00652 \, \text{atm} \)
2. Sum the partial pressures to find the total pressure:
[tex]\[ \text{Total Pressure} = P_{O_2} + P_{N_2} + P_{Ar} \][/tex]
3. Add the values:
[tex]\[ \text{Total Pressure} = 0.875 \, \text{atm} + 0.0553 \, \text{atm} + 0.00652 \, \text{atm} \][/tex]
4. Combine the partial pressures:
[tex]\[ \text{Total Pressure} = 0.93702 \, \text{atm} \][/tex]
5. Round the result to the appropriate number of significant figures (3 decimal places suggested by the data precision):
[tex]\[ \text{Total Pressure} \approx 0.937 \, \text{atm} \][/tex]
Therefore, the total pressure of the mixture is approximately \(0.937 \, \text{atm}\). The answer closest to this value from the provided options is:
B. [tex]\(0.937 \, \text{atm}\)[/tex]
Given the partial pressures:
- Oxygen (\(O_2\)): \(0.875 \, \text{atm}\)
- Nitrogen (\(N_2\)): \(0.0553 \, \text{atm}\)
- Argon (\(Ar\)): \(0.00652 \, \text{atm}\)
Step-by-step solution:
1. Identify the partial pressures:
- \( P_{O_2} = 0.875 \, \text{atm} \)
- \( P_{N_2} = 0.0553 \, \text{atm} \)
- \( P_{Ar} = 0.00652 \, \text{atm} \)
2. Sum the partial pressures to find the total pressure:
[tex]\[ \text{Total Pressure} = P_{O_2} + P_{N_2} + P_{Ar} \][/tex]
3. Add the values:
[tex]\[ \text{Total Pressure} = 0.875 \, \text{atm} + 0.0553 \, \text{atm} + 0.00652 \, \text{atm} \][/tex]
4. Combine the partial pressures:
[tex]\[ \text{Total Pressure} = 0.93702 \, \text{atm} \][/tex]
5. Round the result to the appropriate number of significant figures (3 decimal places suggested by the data precision):
[tex]\[ \text{Total Pressure} \approx 0.937 \, \text{atm} \][/tex]
Therefore, the total pressure of the mixture is approximately \(0.937 \, \text{atm}\). The answer closest to this value from the provided options is:
B. [tex]\(0.937 \, \text{atm}\)[/tex]
