The equilibrium constant \(K_{\mathrm{p}}\) for the reaction $$ \mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g) $$ at \(700^{\circ} \mathrm{C}\) is \(0.76 .\) Detemine the initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of \(1.20 \mathrm{~atm}\) at \(700^{\circ} \mathrm{C}\).

An ICE table allows us to keep track of the Initial, Change, and Equilibrium concentrations or pressures of the species in a chemical reaction. For this reaction, we have: \(CCl_4 (g) \rightleftharpoons C (s) + 2Cl_2 (g)\) Let the initial pressure of the CCl4 be P. Since we are solving for the initial pressure, we'll leave it as P, and the initial pressure of Cl2 will be 0. The change in pressure for C's solid does not influence the equilibrium constant, so we do not need to track it. ICE table: CCl4 C Cl2 Initial P 0 0 Change -x - 2x Equilibrium P-x - 2x At equilibrium, the total pressure is given as 1.20 atm.

The equilibrium constant expression can be written using the equilibrium pressures. Since the carbon is in solid form, it is not included in the equilibrium constant expression. Kp is given as 0.76. Kp = (\( \frac {[Cl_2]^2} {[CCl_4]} \)) = 0.76

Now we will substitute the equilibrium pressures from the ICE table into the equilibrium constant expression. 0.76 = (\( \frac {(2x)^2} {P-x} \))

Given that the total equilibrium pressure is 1.20 atm, we can write an equation for it. 1.20 atm = (P-x) + 2x Now, we can solve for x from the equilibrium constant expression, and substitute it into the equation for the total equilibrium pressure to get the initial pressure, P. From the equilibrium constant expression: x = 0.60 P = 1.80 atm The initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 atm at 700°C is 1.80 atm.