A sample of nitrosyl bromide (NOBr) decomposes according to the equation 2 NOBr(𝑔) ⇌ 2 NO(𝑔) + Br2(𝑔) An equilibrium mixture in a 5.00-L vessel at 100°C contains 3.22 g of NOBr, 3.08 g of NO, and 4.19 g of Br2. (b) What is the total pressure exerted by the mixture of gases?
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Calculate the number of moles of each gas present in the mixture using the formula: number of moles (n) = mass (g) / molar mass (g/mol). The molar masses are: NOBr = 106.92 g/mol, NO = 30.01 g/mol, Br<sub>2</sub> = 159.808 g/mol.
Use the ideal gas law to find the total number of moles of gas in the vessel. The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
Calculate the total pressure using the ideal gas law rearranged to solve for P: P = (nRT) / V. Substitute the total number of moles calculated, the gas constant, the temperature in Kelvin, and the volume of the vessel.
Ensure all units are consistent when substituting values into the ideal gas law equation to calculate the pressure in atmospheres.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the total pressure of a gas mixture, as it allows us to determine how the quantities of gases present affect the overall pressure in a given volume.
To find the total pressure exerted by the gas mixture, it is necessary to convert the mass of each gas into moles using their respective molar masses. This conversion is crucial because the Ideal Gas Law requires the number of moles (n) to calculate pressure, making it a fundamental step in solving the problem.
Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas. This principle is important for determining the total pressure in the vessel, as it allows us to calculate the contribution of each gas based on its mole fraction and the total number of moles present.
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