A mixture of 1.441 g of H2 and 70.24 g of Br2 is heated in a 2.00-L vessel at 700 K. These substances react as follows.
H2(g) + Br2(g) arrow 2 HBr(g)
At equilibrium the vessel is found to contain 0.627 g of H2.
calculate their equilibrium concentrations and Kc
mols H2 @ equil = 0.627g/2 = 0.3135
M H2 @ equil = 0.3135/2L = 0.1567M
M H2 begin = (1.441/4) = 0.360M
M Br2 begin = (70.24/159.8) = 0.440M
........H2 + Br2 ==> 2HBr
I.....0.36..0.44.....0
C.....-x.....-x.......2x
E...0.36-x..0.44-x...2x
At equil (H2) = 0.157M; therefore, we know
0.36-x = 0.157 and we solve for x. Use that to calculate each of the equilibrium values, substitute those into the Kc expression and calculate Kc.
Be sure and check (confirm) those numbers. I just ran them one time on my calculator.
To determine the equilibrium concentrations and Kc for the given reaction, we need to follow a step-by-step approach.
Step 1: Calculate the moles of each substance involved.
We have the initial amount of H2 (1.441 g) and Br2 (70.24 g). To calculate the number of moles, we use the molar mass of each substance.
Molar mass of H2 = 2 g/mol
Molar mass of Br2 = 159.8 g/mol
Moles of H2 = (1.441 g) / (2 g/mol) = 0.7205 mol
Moles of Br2 = (70.24 g) / (159.8 g/mol) = 0.4392 mol
Step 2: Use stoichiometry to determine the change in moles.
From the balanced equation, we can see that the stoichiometric ratio between H2 and HBr is 1:2. This means that for every 1 mole of H2, we will produce 2 moles of HBr.
Change in moles of H2 = initial moles of H2 - moles of H2 at equilibrium
Change in moles of H2 = 0.7205 mol - 0.627 g / (2 g/mol) = 0.7205 mol - 0.3135 mol = 0.407 mol
Since 1 mole of H2 reacts to produce 2 moles of HBr, we have a change in moles of HBr equal to 2 times the change in moles of H2.
Change in moles of HBr = 2 × (0.407 mol) = 0.814 mol
Step 3: Calculate the equilibrium concentrations.
The total volume of the vessel is given as 2.00 L. We can use this information to determine the concentration of each substance using the moles calculated in Step 2.
Concentration of H2 = moles of H2 / volume of vessel = 0.407 mol / 2.00 L = 0.2035 M
Concentration of Br2 = moles of Br2 / volume of vessel = 0.4392 mol / 2.00 L = 0.2196 M
Concentration of HBr = moles of HBr / volume of vessel = 0.814 mol / 2.00 L = 0.407 M
Step 4: Calculate the equilibrium constant (Kc).
The equilibrium constant, Kc, can be determined by comparing the molar concentrations of the products and reactants using the balanced equation.
Kc = (concentration of HBr)^2 / (concentration of H2 × concentration of Br2)
Kc = (0.407 M)^2 / (0.2035 M × 0.2196 M)
Kc = 8.3527 / 0.044766
Kc = 186.4 (rounded to one decimal place)
Therefore, the equilibrium concentrations of H2, Br2, and HBr are 0.2035 M, 0.2196 M, and 0.407 M, respectively. The equilibrium constant, Kc, is 186.4.