To calculate the total pressure in a container with three different gases, we must sum up the partial pressures of each gas. However, before we do that, we must ensure that all pressures are in the same units. The common units for pressure are Pascals (Pa), kilopascals (kPa), atmospheres (atm), or millimeters of mercury (mmHg). Here, we have pressures in kPa, mmHg, and atm. Let's convert all pressures to kPa to find the total pressure.
We have the following conversions:
- 1 atm = 101.325 kPa
- 1 mmHg = 0.133322 kPa (since 1 atm = 760 mmHg)
Now, let's convert the pressures to kPa:
1. The pressure of the first gas is already in kPa:
[tex]\( P_1 = 44.5 \text{ kPa} \)[/tex]
2. To convert the pressure from mmHg to kPa:
[tex]\( P_2 = 823 \text{ mmHg} \times 0.133322 \text{ kPa/mmHg} \)[/tex]
Let's calculate [tex]\( P_2 \)[/tex]:
[tex]\( P_2 = 823 \times 0.133322 \)[/tex]
[tex]\( P_2 \approx 109.68 \text{ kPa} \)[/tex] (rounding to two decimal places)
3. To convert the pressure from atm to kPa:
[tex]\( P_3 = 3.11 \text{ atm} \times 101.325 \text{ kPa/atm} \)[/tex]
Let's calculate [tex]\( P_3 \)[/tex]:
[tex]\( P_3 = 3.11 \times 101.325 \)[/tex]
[tex]\( P_3 \approx 315.12 \text{ kPa} \)[/tex] (rounding to two decimal places)
Now, we sum up all the partial pressures in kPa to get the total pressure:
[tex]\( P_{total} = P_1 + P_2 + P_3 \)[/tex]
[tex]\( P_{total} = 44.5 \text{ kPa} + 109.68 \text{ kPa} + 315.12 \text{ kPa} \)[/tex]
[tex]\( P_{total} \approx 469.3 \text{ kPa} \)[/tex]
The total pressure in the container is approximately 469.3 kPa.
