If \( \mathrm{N}_{2} \) is added to a balloon that contains 380.0 mmHg of \( \mathrm{O}_{2} \) and 130.0 mmHg of \( \mathrm{CO}_{2} \) to give a total pressure of 950.0 mmHg , what is the partial pressure of each gas in the final mixture? Be sure each of your answer entries has the correct number of significant figures. Part 1 of 3 Part 2 of 3 \( P_{\mathrm{C}_{2}}= \) \( P_{\mathrm{CO}_{2}}= \)
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To find the partial pressure of each gas in the final mixture, we can use Dalton’s Law of Partial Pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas. 1. We have the total pressure after adding \( \mathrm{N}_2 \): \[ P_{\text{total}} = 950.0 \, \text{mmHg} \] 2. The partial pressures before adding \( \mathrm{N}_2 \) are: - \( P_{\mathrm{O}_2} = 380.0 \, \text{mmHg} \) - \( P_{\mathrm{CO}_2} = 130.0 \, \text{mmHg} \) 3. The total pressure from the existing gases before adding \( \mathrm{N}_2 \): \[ P_{\text{existing gases}} = P_{\mathrm{O}_2} + P_{\mathrm{CO}_2} = 380.0 \, \text{mmHg} + 130.0 \, \text{mmHg} = 510.0 \, \text{mmHg} \] 4. The partial pressure of \( \mathrm{N}_2 \): \[ P_{\mathrm{N}_2} = P_{\text{total}} - P_{\text{existing gases}} = 950.0 \, \text{mmHg} - 510.0 \, \text{mmHg} = 440.0 \, \text{mmHg} \] Now we have the partial pressures as follows: \[ P_{\mathrm{O}_2} = 380.0 \, \text{mmHg} \] \[ P_{\mathrm{CO}_2} = 130.0 \, \text{mmHg} \] \[ P_{\mathrm{N}_2} = 440.0 \, \text{mmHg} \] So in summary: \( P_{\mathrm{O}_2} = 380.0 \, \text{mmHg} \) \( P_{\mathrm{CO}_2} = 130.0 \, \text{mmHg} \)
