Answer :
Certainly! Let's solve the problem step-by-step:
When a chemist collects hydrogen gas over water, the gas collected is actually a mixture of hydrogen gas and water vapor. According to Dalton's Law of Partial Pressures, the total pressure in a container is the sum of the partial pressures of all the individual gases present.
Here's how to solve the problem:
1. Total Pressure in the Collecting Bottle:
- The total pressure inside the collecting bottle is given as 97.1 kilopascals (kPa).
2. Vapor Pressure of Water:
- The pressure exerted by water vapor in the collecting bottle is given as 3.2 kilopascals (kPa).
3. Apply Dalton’s Law of Partial Pressures:
- Dalton’s Law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.
- Mathematically, this can be expressed as:
[tex]\[
P_{\text{total}} = P_{\text{hydrogen}} + P_{\text{water vapor}}
\][/tex]
- We want to find the partial pressure of hydrogen ([tex]\(P_{\text{hydrogen}}\)[/tex]).
4. Calculate the Partial Pressure of Hydrogen:
- Rearrange the equation to solve for the partial pressure of hydrogen:
[tex]\[
P_{\text{hydrogen}} = P_{\text{total}} - P_{\text{water vapor}}
\][/tex]
- Substitute the known values:
[tex]\[
P_{\text{hydrogen}} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa}
\][/tex]
- Perform the subtraction:
[tex]\[
P_{\text{hydrogen}} = 93.9 \, \text{kPa}
\][/tex]
Therefore, the partial pressure of the hydrogen gas is 93.9 kPa, which corresponds to option A.
When a chemist collects hydrogen gas over water, the gas collected is actually a mixture of hydrogen gas and water vapor. According to Dalton's Law of Partial Pressures, the total pressure in a container is the sum of the partial pressures of all the individual gases present.
Here's how to solve the problem:
1. Total Pressure in the Collecting Bottle:
- The total pressure inside the collecting bottle is given as 97.1 kilopascals (kPa).
2. Vapor Pressure of Water:
- The pressure exerted by water vapor in the collecting bottle is given as 3.2 kilopascals (kPa).
3. Apply Dalton’s Law of Partial Pressures:
- Dalton’s Law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.
- Mathematically, this can be expressed as:
[tex]\[
P_{\text{total}} = P_{\text{hydrogen}} + P_{\text{water vapor}}
\][/tex]
- We want to find the partial pressure of hydrogen ([tex]\(P_{\text{hydrogen}}\)[/tex]).
4. Calculate the Partial Pressure of Hydrogen:
- Rearrange the equation to solve for the partial pressure of hydrogen:
[tex]\[
P_{\text{hydrogen}} = P_{\text{total}} - P_{\text{water vapor}}
\][/tex]
- Substitute the known values:
[tex]\[
P_{\text{hydrogen}} = 97.1 \, \text{kPa} - 3.2 \, \text{kPa}
\][/tex]
- Perform the subtraction:
[tex]\[
P_{\text{hydrogen}} = 93.9 \, \text{kPa}
\][/tex]
Therefore, the partial pressure of the hydrogen gas is 93.9 kPa, which corresponds to option A.
