Question

Sulfur dioxide and oxygen react to form sulfur trioxide during one of the key steps in sulfuric acid synthesis. An industrial chemist studying this reaction fills a 25.0L tank with 4.5 mol of sulfur dioxide gas and 4.5 mol of oxygen gas at 30.°C. He then raises the temperature, and when the mixture has come to equilibrium measures the amount of sulfur trioxide gas to be 1.4 mol. Calculate the concentration equilibrium constant for the reaction of sulfur dioxide and oxygen at the final temperature of the mixture. Round your answer to 2 significant digits.

Answer 1

To calculate the concentration equilibrium constant (Kc) for the reaction of SO2 and O2 to form SO3, find the equilibrium concentrations from the initial amounts and amount at equilibrium, then apply the equilibrium expression. The resulting Kc for the reaction at the final temperature is 0.020 when rounded to two significant digits.

Step-by-step explanation:

The calculation of the concentration equilibrium constant for the reaction between sulfur dioxide and oxygen to form sulfur trioxide at a certain temperature involves using the equilibrium concentrations of reactants and products. The balanced chemical equation for the reaction is:

2 SO2(g) + O2(g) = 2 SO3(g)

Given 4.5 mol of SO2 and 4.5 mol of O2 initially in a 25.0 L tank, and 1.4 mol of SO3 at equilibrium, we can calculate the change in moles during the reaction (δ) and thus the equilibrium concentrations ([SO2], [O2], and [SO3]). The concentration equilibrium constant (Kc) is then found using the expression:

Kc = ([SO3]2)/([SO2]2 × [O2])

Through stoichiometry and equilibrium concentration calculations, the concentrations are:

[SO3] = 1.4 mol / 25.0 L = 0.056 M

[SO2] = (4.5 mol - 1.4 mol) / 25.0 L = 0.124 M (since 1 mol of SO2 is consumed for every mol of SO3 produced)

[O2] = (4.5 mol - 0.7 mol) / 25.0 L = 0.152 M (since 0.5 mol of O2 is consumed for every mol of SO3 produced)

Plugging these values into the Kc expression gives:

Kc = (0.0562) / (0.1242 × 0.152) = 0.0197

The calculated Kc at the final temperature is 0.020 (rounded to two significant digits).

Answer 2

1.3 is the concentration equilibrium constant for the reaction of sulfur dioxide and oxygen at the final temperature of the mixture.

Step-by-step explanation:

Initial Concentration of sulfur dioxide =
`[SO_2]=(4.5 mol)/(25 L)=0.18 M`

Initial Concentration of oxygen=
`[O_2]=(4.5 mol)/(25 L)=0.18 M`

`2SO_2+O_2\rightleftharpoons 2SO_3`

Initially (0.18 M) (0.18 M) 0

Eq'm (0.18 -2x) (0.18 -x) 2x

Equilibrium concentration of sulfur trioxide =
`[SO_3]=2x=(1.4 mol)/(25 L)=0.056 M`

x = 0.028 M

Equilibrium concentration of sulfur dioxide =
`[SO_2]'=(0.18 -2x)=0.18 - 0.056 =0.124 M`

Equilibrium concentration of oxygen=
`[O_2]'=(0.18 -x)=0.18 - 0.028 =0.152 M`

The expression for an equilibrium constant will be :

`K_c=([SO_3]^2)/([SO_2]'^2[O_2]')`

`K_c=((0.056 M)^2)/((0.124 M)^2(0.152 M))=1.3418\approx 1.3`

1.3 is the concentration equilibrium constant for the reaction of sulfur dioxide and oxygen at the final temperature of the mixture.