At a certain temperature, a 19.0-L contains holds four gases in equilibrium. Their masses are: 3.5 g SO3, 4.6 g SO2, 14.0 g N2, and 0.98 g N2O. What is the value of the equilibrium constant at this temperature for the reaction of SO2 with N2O to form SO3 and N2 (balanced with lowest whole-number coefficients)?
To determine the value of the equilibrium constant at a certain temperature, we need to use the balanced equation for the reaction and the molar concentrations of the gases involved.
The balanced equation for the reaction is:
SO2 + N2O -> SO3 + N2
To find the molar concentrations of the gases, we need to convert the given masses into moles. This can be done using the molar mass of each substance.
Molar mass of SO2 = 64.06 g/mol
Molar mass of N2O = 44.01 g/mol
Molar mass of SO3 = 80.06 g/mol
Molar mass of N2 = 28.01 g/mol
Now, let's calculate the moles of each gas:
Moles of SO2 = Mass of SO2 / Molar mass of SO2 = 4.6 g / 64.06 g/mol
Moles of N2O = Mass of N2O / Molar mass of N2O = 0.98 g / 44.01 g/mol
Moles of SO3 = Mass of SO3 / Molar mass of SO3 = 3.5 g / 80.06 g/mol
Moles of N2 = Mass of N2 / Molar mass of N2 = 14.0 g / 28.01 g/mol
Next, we need to calculate the molar concentrations of the gases. This can be done by dividing the moles by the volume in liters.
Molar concentration (c) = Moles of gas / Volume of container
Using the given volume of 19.0 L, we can calculate the molar concentrations of each gas:
Concentration of SO2 = Moles of SO2 / Volume of container = Moles of SO2 / 19.0 L
Concentration of N2O = Moles of N2O / Volume of container = Moles of N2O / 19.0 L
Concentration of SO3 = Moles of SO3 / Volume of container = Moles of SO3 / 19.0 L
Concentration of N2 = Moles of N2 / Volume of container = Moles of N2 / 19.0 L
Now that we have the molar concentrations of each gas, we can plug these values into the equilibrium constant expression.
Equilibrium constant (K) = [concentration of SO3] * [concentration of N2] / [concentration of SO2] * [concentration of N2O]
Substituting the molar concentrations we calculated earlier:
K = ([Moles of SO3 / 19.0 L] * [Moles of N2 / 19.0 L]) / ([Moles of SO2 / 19.0 L] * [Moles of N2O / 19.0 L])
Finally, simplify the expression by canceling out the volume terms:
K = (Moles of SO3 * Moles of N2) / (Moles of SO2 * Moles of N2O)
Now, plug in the values of the moles we calculated earlier and calculate K.