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A certain laser uses a gas mixture consisting of 9.00 g HCl, 2.00 g H2, and 165.0 g of Ne. What pressure is exerted by the mixture in a 75.0-L tank at 228C? Which gas has the smallest partial pressure?

Short Answer

Expert verified
Answer: The total pressure exerted by the gas mixture is 31.271 atm, and Hydrogen Chloride (HCl) has the smallest partial pressure, with a value of 0.8154 atm.

Step by step solution

01

Calculate the number of moles for each gas

Divide the given mass of each gas by its molar mass. Molar mass of HCl = 36.5 g/mol, molar mass of H2 = 2.0 g/mol, molar mass of Ne = 20.2 g/mol. n_HCl = (9.00 g) / (36.5 g/mol) = 0.2466 mol n_H2 = (2.00 g) / (2.0 g/mol) = 1.000 mol n_Ne = (165.0 g) / (20.2 g/mol) = 8.1683 mol
02

Convert the temperature to Kelvin

We convert the given temperature from Celsius to Kelvin to use it in the Ideal Gas Law formula. T_K = 228 + 273.15 = 501.15 K
03

Apply Ideal Gas Law for each gas to find partial pressures

Use the Ideal Gas Law formula, PV = nRT, for each gas where R is the gas constant (0.0821 L.atm/mol.K) and V is the volume of the tank (75.0 L). P_HCl = (n_HCl * R * T_K) / V = (0.2466 mol * 0.0821 L.atm/mol.K * 501.15 K) / 75.0 L = 0.8154 atm P_H2 = (n_H2 * R * T_K) / V = (1.000 mol * 0.0821 L.atm/mol.K * 501.15 K) / 75.0 L = 3.3928 atm P_Ne = (n_Ne * R * T_K) / V = (8.1683 mol * 0.0821 L.atm/mol.K * 501.15 K) / 75.0 L = 27.0628 atm
04

Calculate the total pressure exerted by the mixture

Find the total pressure using Dalton's Law, P_total = P_HCl + P_H2 + P_Ne. P_total = 0.8154 atm + 3.3928 atm + 27.0628 atm = 31.271 atm
05

Determine the gas with the smallest partial pressure

Compare the partial pressures of HCl, H2, and Ne to determine the gas with the smallest partial pressure. The smallest partial pressure is P_HCl = 0.8154 atm. The total pressure exerted by the gas mixture is 31.271 atm, and the gas with the smallest partial pressure is HCl.

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