Calculate the equilibrium constant for the following reaction at 100°C.
2 TiCl3(g)+2 HCl (g) = 2 TiCl4(g)+H2(g)
∆G°rxn = + 47.0 kJ mol-1
cant i just use K = e^ -Delta G/RT? --> K = e ^ -47.0 kJ mol-1 /(8.314)(273+100)?
what is the point of having the balanced equation?
or am i not supposed to use that formula at all
The way I see it is that you have a reaction that is dGo = 47.0 kJ/mol and you have two moles which makes it 94 kJ for the reaction as written.
Yes, you can use the formula K = e^(-ΔG/RT) to calculate the equilibrium constant (K) at a given temperature. However, it seems like there may be a misunderstanding in the calculation you have written.
To properly calculate K using the formula, you need to take the negative of the change in Gibbs free energy (∆G°rxn) and divide it by the gas constant (R) multiplied by the temperature (T) in Kelvin.
Let's go through the correct calculation step by step:
1. Convert the temperature from Celsius to Kelvin: 100°C + 273.15 = 373.15 K.
2. Convert the given ∆G°rxn from kilojoules to joules: 47.0 kJ/mol * 1000 J/kJ = 47,000 J/mol.
3. Plug the values into the equation: K = e^(-ΔG°rxn / (RT))
K = e^(-47,000 J/mol / (8.314 J/(mol·K) * 373.15 K))
Now, regarding the significance of the balanced equation: The balanced equation is crucial in determining the stoichiometry and molar ratios between the reactants and products. When you have a balanced equation, you will be able to identify the coefficients in front of each substance, which indicate the relative number of moles involved in the reaction.
In the case of the reaction you provided, the balanced equation tells us that for every 2 moles of TiCl3 and HCl, we get 2 moles of TiCl4 and 1 mole of H2. These coefficients are important when calculating the equilibrium constant because K expresses the ratio of the concentrations (or partial pressures) of the products to the concentrations (or partial pressures) of the reactants at equilibrium.
So, the balanced equation gives us the necessary information to determine the stoichiometry and properly express the equilibrium constant.