Question

A sample of nitrosyl bromide (NOBr) decomposes according to the equation $$ 2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) $$ An equilibrium mixture in a 5.00-L vessel at \(100^{\circ} \mathrm{C}\) contains \(3.22 \mathrm{~g}\) of \(\mathrm{NOBr}, 3.08 \mathrm{~g}\) of \(\mathrm{NO}\), and \(4.19 \mathrm{~g}\) of \(\mathrm{Br}_{2}\). (a) Calculate \(K_{c}\). (b) What is the total pressure exerted by the mixture of gases?

Short answer

The equilibrium constant, Kc, for the reaction is 24.15, and the total pressure exerted by the mixture of gases is 1.024 atm.

Step-by-step solution

Convert grams to moles

To calculate Kc, we need the molar concentrations of the chemical species involved. First, let's convert the given masses to moles using the molar mass of each compound: For NOBr: Molar mass = 14.01 (N) + 15.99 (O) + 79.90 (Br) = 109.90 g/mol Moles of NOBr = (3.22 g) / (109.90 g/mol) = 0.0293 mol For NO: Molar mass = 14.01 (N) + 15.99 (O) = 30 g/mol Moles of NO = (3.08 g) / (30 g/mol) = 0.1027 mol For Br2: Molar mass = 2(79.90) = 159.8 g/mol Moles of Br2 = (4.19 g) / (159.8 g/mol) = 0.0262 mol

Calculate molar concentrations

Using the given volume of the vessel (5.00 L) and the moles calculated in Step 1, calculate the molar concentrations: [NOBr] = (0.0293 mol) / (5.00 L) = 0.00586 mol/L [NO] = (0.1027 mol) / (5.00 L) = 0.02054 mol/L [Br2] = (0.0262 mol) / (5.00 L) = 0.00524 mol/L

Calculate the equilibrium constant, Kc

The balanced chemical equation is: 2 NOBr(g) ⇌ 2 NO(g) + Br2(g) The expression for the equilibrium constant, Kc, is given by: Kc = ([NO]^2 * [Br2]) / ([NOBr]^2) Now plug in the concentrations we calculated in Step 2: Kc = ((0.02054)^2 * (0.00524))/((0.00586)^2) = 24.15 Therefore, Kc = 24.15

Calculate total pressure

To calculate the total pressure exerted by the mixture of gases, we will use the Ideal Gas Law: PV = nRT In this case, we will add up the number of moles for all the gases (n_total) and use the given temperature (100°C which is 373.15 K) and the volume (5.00 L). n_total = 0.0293 + 0.1027 + 0.0262 = 0.1582 mol Now, use the value of the gas constant, R = 0.0821 L⋅atm/(mol⋅K), and plug all values: P = (nRT) / V P = (0.1582 mol * 0.0821 L⋅atm/(mol⋅K) * 373.15 K) / 5.00 L P = 1.024 atm The total pressure exerted by the mixture of gases is 1.024 atm.