Answer :
The partial pressure of Gas 3 is 5.8 kPa.
To find the partial pressure of Gas 3 in a mixture of gases at standard temperature and pressure (STP), we use Dalton's Law of Partial Pressures. According to Dalton's Law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
At STP, the total pressure of the gas mixture is 101.3 kPa (standard atmospheric pressure).
Given:
- Partial pressure of Gas 1: [tex]\( P_1 = 56.4 \) kPa[/tex]
- Partial pressure of Gas 2: [tex]\( P_2 = 39.1 \) kPa[/tex]
Let's denote the partial pressure of Gas 3 as [tex]\( P_3 \)[/tex].
According to Dalton's Law:
[tex]\[ P_{\text{total}} = P_1 + P_2 + P_3 \][/tex]
Substitute the known values:
[tex]\[ 101.3 \, \text{kPa} = 56.4 \, \text{kPa} + 39.1 \, \text{kPa} + P_3 \][/tex]
Solve for [tex]\( P_3 \)[/tex]:
[tex]\[ P_3 = 101.3 \, \text{kPa} - 56.4 \, \text{kPa} - 39.1 \, \text{kPa} \][/tex]
[tex]\[ P_3 = 101.3 \, \text{kPa} - 95.5 \, \text{kPa} \][/tex]
[tex]\[ P_3 = 5.8 \, \text{kPa} \][/tex]
Final answer:
Dalton's Law of Partial Pressures states that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases. In this case, the partial pressure of Gas 3 can be found by subtracting the sum of the partial pressures of Gas 1 and Gas 2 from the total pressure. The partial pressure of Gas 3 is 96.5 kPa.
Explanation:
Dalton's Law of Partial Pressures states that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases. In this case, Gas 1 has a partial pressure of 56.4 kPa and Gas 2 has a partial pressure of 39.1 kPa. Therefore, the partial pressure of Gas 3 can be found by subtracting the sum of the partial pressures of Gas 1 and Gas 2 from the total pressure.
Partial Pressure of Gas 3 = Total Pressure - Partial Pressure of Gas 1 - Partial Pressure of Gas 2
Partial Pressure of Gas 3 = 192 kPa - 56.4 kPa - 39.1 kPa = 96.5 kPa
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