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Chapter 10: Problem 63

A mixture containing $0.50 \mathrm{~mol} \mathrm{H}_{2}(g), 1.00 \mathrm{~mol} \mathrm{O}_{2}(g)\(, and 3.50 \)\mathrm{mol} \mathrm{N}_{2}(g)$ is confined in a 25.0-L vessel at \(25^{\circ} \mathrm{C}\). (a) Calculate the total pressure of the mixture. (b) Calculate the partial pressure of each of the gases in the mixture.

Short Answer

Expert verified
(a) The total pressure of the gaseous mixture is 9.86 atm. (b) The partial pressures of each gas are: H₂: 0.986 atm, O₂: 1.972 atm, and N₂: 6.902 atm.

Step by step solution

01

Convert the temperature to Kelvin

First, we need to convert the given temperature from Celsius to Kelvin. To do this, we will add 273.15 to the given value: Temperature in Kelvin = 25°C + 273.15 = 298.15 K
02

Use Ideal Gas Law for the total pressure

We will use the Ideal Gas Law to calculate the total pressure of the mixture: PV = nRT Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L atm/mol K), and T is the temperature in Kelvin. Since we have a mixture, we will need to find the total number of moles. Thus: Total Moles (n) = Moles of H₂ + Moles of O₂ + Moles of N₂ = 0.50 + 1.00 + 3.50 = 5.00 moles Now that we know the total moles, we can solve for the total pressure P: P = nRT / V
03

Calculate the total pressure

Substitute the values for n, R, T, and V into the equation to find the total pressure: P = (5.00 moles) x (0.0821 L atm/mol K) x (298.15 K) / (25.0 L) = 9.86 atm Thus, the total pressure of the mixture is 9.86 atm.
04

Calculate the mole fractions of each gas

To find the partial pressure of each gas, we need to find the mole fraction of each gas in the mixture. The mole fraction is defined as the number of moles of a specific component divided by the total number of moles in the mixture: Mole fraction for H₂ (x_H2) = Moles of H₂ / Total moles = 0.50 / 5.00 = 0.10 Mole fraction for O₂ (x_O2) = Moles of O₂ / Total moles = 1.00 / 5.00 = 0.20 Mole fraction for N₂ (x_N2) = Moles of N₂ / Total moles = 3.50 / 5.00 = 0.70
05

Calculate the partial pressures of each gas

Now we can find the partial pressure of each gas by multiplying the mole fraction of each gas by the total pressure: Partial Pressure of H₂ (P_H2) = x_H2 x P = 0.10 × 9.86 atm = 0.986 atm Partial Pressure of O₂ (P_O2) = x_O2 x P = 0.20 × 9.86 atm = 1.972 atm Partial Pressure of N₂ (P_N2) = x_N2 x P = 0.70 × 9.86 atm = 6.902 atm
06

Summary of the Results

In conclusion, (a) The total pressure of the gaseous mixture is: 9.86 atm (b) The partial pressures of each gas are: - H₂: 0.986 atm - O₂: 1.972 atm - N₂: 6.902 atm

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Most popular questions from this chapter

A piece of dry ice (solid carbon dioxide) with a mass of \(20.0 \mathrm{~g}\) is placed in a 25.0-L vessel that already contains air at \(50.66 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant \(\mathrm{CO}_{2}\) gas, and the total pressure in the container at \(25^{\circ} \mathrm{C} ?\)

Calculate each of the following quantities for an ideal gas: (a) the volume of the gas, in liters, if \(1.50 \mathrm{~mol}\) has a pressure of $126.7 \mathrm{kPa}\( at a temperature of \)-6^{\circ} \mathrm{C} ;(\mathbf{b})$ the absolute temperature of the gas at which \(3.33 \times 10^{-3}\) mol occupies \(478 \mathrm{~mL}\) at \(99.99 \mathrm{kPa} ;(\mathbf{c})\) the pressure, in pascals, if \(0.00245 \mathrm{~mol}\) occupies \(413 \mathrm{~mL}\) at \(138^{\circ} \mathrm{C} ;(\mathbf{d})\) the quantity of gas, in moles, if 126.5 L at \(54^{\circ} \mathrm{C}\) has a pressure of \(11.25 \mathrm{kPa}\).

Nickel carbonyl, \(\mathrm{Ni}(\mathrm{CO})_{4},\) is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8 -hr workday is \(1 \mathrm{ppb}\) (parts per billion) by volume, which means that there is one mole of \(\mathrm{Ni}(\mathrm{CO})_{4}\) for every \(10^{9}\) moles of gas. Assume \(24^{\circ} \mathrm{C}\) and 101.3 kPa pressure. What mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) is allowable in a laboratory room that is \(3.5 \mathrm{~m} \times 6.0 \mathrm{~m} \times 2.5 \mathrm{~m} ?\)

Which of the following statements is false? (a) Gases are far less dense than liquids. (b) Gases are far more compressible than liquids. (c) Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors. (d) The volume occupied by a gas is determined by the volume of its container.

Suppose you have a fixed amount of an ideal gas at a constant volume. If the pressure of the gas is doubled while the volume is held constant, what happens to its temperature? [Section 10.4\(]\)
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