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Chapter 10: Problem 64

A deep-sea diver uses a gas cylinder with a volume of 10.0 \(\mathrm{L}\) and a content of 51.2 \(\mathrm{g}\) of \(\mathrm{O}_{2}\) and 32.6 \(\mathrm{g}\) of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is \(19^{\circ} \mathrm{C}\) .

Short Answer

Expert verified
The partial pressure of O2 is 3.8108 atm, the partial pressure of He is 19.7326 atm, and the total pressure inside the gas cylinder is 23.5434 atm.

Step by step solution

01

Convert masses to moles

We need to convert the mass of O2 and He gases given in grams to moles. To do this, we will use the molar masses of O2 and He. The molar mass of O2 = 32 g/mol. The molar mass of He = 4 g/mol. Moles of O2 = (mass of O2) / (molar mass of O2) Moles of O2 = (51.2 g) / (32 g/mol) = 1.6 mol Moles of He = (mass of He) / (molar mass of He) Moles of He = (32.6 g) / (4 g/mol) = 8.15 mol
02

Convert temperature to Kelvin

The given temperature is in Celsius. We need to convert it to Kelvin. Temperature in Kelvin = Temperature in Celsius + 273.15 Temperature = 19°C + 273.15 = 292.15 K
03

Find partial pressures of O2 and He

Now we will use the Ideal Gas Law to find the partial pressures of O2 and He. PV = nRT P = (nRT) / V Partial pressure of O2, P_O2 = (n_O2 * R * T)/V P_O2 = (1.6 mol * 0.0821 L·atm/mol·K * 292.15 K) / 10.0 L P_O2 = 3.8108 atm Partial pressure of He, P_He = (n_He * R * T)/V P_He = \( (8.15 \text{ mol} \times 0.0821 \text{ L·atm/mol·K} \times 292.15 \text{ K})/(10.0 \text{ L})\) P_He = 19.7326 atm
04

Find total pressure

To find the total pressure, we will add the partial pressures of O2 and He. Total pressure, P_total = P_O2 + P_He P_total = 3.8108 atm + 19.7326 atm = 23.5434 atm So, the partial pressure of O2 is 3.8108 atm, the partial pressure of He is 19.7326 atm, and the total pressure inside the gas cylinder is 23.5434 atm.

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Most popular questions from this chapter

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