Answer :
To determine the partial pressure of oxygen in the scuba diver's air tank, we will use Dalton's Law of Partial Pressures. According to this law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Mathematically, it can be expressed as:
[tex]\[ P_{\text{total}} = P_{\text{nitrogen}} + P_{\text{helium}} + P_{\text{oxygen}} \][/tex]
Let’s break this down step-by-step using the given values:
1. Total pressure, [tex]\( P_{\text{total}} \)[/tex], is 205 atmospheres.
2. Partial pressure of nitrogen, [tex]\( P_{\text{nitrogen}} \)[/tex], is 143 atmospheres.
3. Partial pressure of helium, [tex]\( P_{\text{helium}} \)[/tex], is 41 atmospheres.
We need to find the partial pressure of oxygen, [tex]\( P_{\text{oxygen}} \)[/tex]. Using the formula from Dalton's Law:
[tex]\[ P_{\text{total}} = P_{\text{nitrogen}} + P_{\text{helium}} + P_{\text{oxygen}} \][/tex]
Substitute the known values into the equation:
[tex]\[ 205 = 143 + 41 + P_{\text{oxygen}} \][/tex]
We can isolate [tex]\( P_{\text{oxygen}} \)[/tex] by rearranging the equation:
[tex]\[ P_{\text{oxygen}} = 205 - 143 - 41 \][/tex]
Subtract the partial pressures of nitrogen and helium from the total pressure:
[tex]\[ P_{\text{oxygen}} = 205 - 143 - 41 \][/tex]
[tex]\[ P_{\text{oxygen}} = 21 \][/tex]
Thus, the partial pressure of oxygen in the tank is [tex]\( 21 \)[/tex] atmospheres, which matches option A.
Therefore, the correct answer is:
A. [tex]\( 21 \)[/tex] atm
[tex]\[ P_{\text{total}} = P_{\text{nitrogen}} + P_{\text{helium}} + P_{\text{oxygen}} \][/tex]
Let’s break this down step-by-step using the given values:
1. Total pressure, [tex]\( P_{\text{total}} \)[/tex], is 205 atmospheres.
2. Partial pressure of nitrogen, [tex]\( P_{\text{nitrogen}} \)[/tex], is 143 atmospheres.
3. Partial pressure of helium, [tex]\( P_{\text{helium}} \)[/tex], is 41 atmospheres.
We need to find the partial pressure of oxygen, [tex]\( P_{\text{oxygen}} \)[/tex]. Using the formula from Dalton's Law:
[tex]\[ P_{\text{total}} = P_{\text{nitrogen}} + P_{\text{helium}} + P_{\text{oxygen}} \][/tex]
Substitute the known values into the equation:
[tex]\[ 205 = 143 + 41 + P_{\text{oxygen}} \][/tex]
We can isolate [tex]\( P_{\text{oxygen}} \)[/tex] by rearranging the equation:
[tex]\[ P_{\text{oxygen}} = 205 - 143 - 41 \][/tex]
Subtract the partial pressures of nitrogen and helium from the total pressure:
[tex]\[ P_{\text{oxygen}} = 205 - 143 - 41 \][/tex]
[tex]\[ P_{\text{oxygen}} = 21 \][/tex]
Thus, the partial pressure of oxygen in the tank is [tex]\( 21 \)[/tex] atmospheres, which matches option A.
Therefore, the correct answer is:
A. [tex]\( 21 \)[/tex] atm
