calculate kc for reaction I2 (g)+Cl2 (g)⇌2ICl(g )Kp=81.9 (at 298 K)
To calculate the equilibrium constant (Kc) for the reaction I2 (g) + Cl2 (g) ⇌ 2ICl (g), where the value of Kp is given as 81.9 at 298 K, you will need to use the relationship between Kp and Kc.
The relationship between Kp and Kc is as follows:
Kp = Kc * (RT)^(Δn)
Where:
Kp is the equilibrium constant in terms of partial pressures,
Kc is the equilibrium constant in terms of molar concentrations,
R is the ideal gas constant (0.0821 L·atm/mol·K),
T is the temperature in Kelvin,
Δn is the difference in moles of gaseous products and reactants (coef. of products - coef. of reactants).
In this case, the equation is already balanced and the reaction involves gases only, so Δn = 2 - (1+1) = 0.
Now, let's rearrange the formula and solve for Kc:
Kc = Kp / (RT)^(Δn)
Substituting the given values:
Kp = 81.9
R = 0.0821 L·atm/mol·K
T = 298 K
Δn = 0
Kc = 81.9 / (0.0821 * 298)^(0)
Simplifying the equation gives us:
Kc = 81.9
Therefore, the equilibrium constant (Kc) for the reaction I2 (g) + Cl2 (g) ⇌ 2ICl (g) is 81.9.
To calculate the equilibrium constant, Kc, for the given reaction, you can use the relationship between Kp (equilibrium constant in terms of partial pressure) and Kc (equilibrium constant in terms of concentration).
The balanced equation for the reaction is:
I2 (g) + Cl2 (g) ⇌ 2ICl (g)
Firstly, let's obtain the expression for Kp using the given value:
Kp = 81.9
Since the reaction is written in terms of gases, Kp is the ratio of the partial pressures of the products raised to their stoichiometric coefficients (2):
Kp = (P_ICl)^2 / (P_I2 * P_Cl2)
Given that Kp = 81.9, we can rewrite the equation as:
81.9 = (P_ICl)^2 / (P_I2 * P_Cl2)
To calculate Kc, we need to relate the partial pressures of the gases to their concentrations using the ideal gas law. For this, we require the value of the total pressure, in this case, at 298 K.
Assuming the total pressure is P_total, you can write:
P_total = P_I2 + P_Cl2 + P_ICl
Now, we can express the partial pressures in terms of their concentrations using the ideal gas law:
P_I2 = [I2] * (R * T / V)
P_Cl2 = [Cl2] * (R * T / V)
P_ICl = [ICl] * (R * T / V)
where [I2], [Cl2], and [ICl] are the concentrations of I2, Cl2, and ICl, respectively, R is the ideal gas constant (0.0821 L atm / mol K), T is the temperature in Kelvin (298 K), and V is the volume of the system.
Substituting these expressions back into the equation for Kp, we get:
81.9 = ([ICl] * (R * T / V))^2 / (([I2] * (R * T / V)) * ([Cl2] * (R * T / V)))
Canceling out the terms involving R, T, and V, we get:
81.9 = ([ICl]^2) / ([I2] * [Cl2])
The expression is now in terms of concentrations. Therefore, the equilibrium constant, Kc, can be written as:
Kc = [ICl]^2 / ([I2] * [Cl2])
Note that the concentrations, [I2], [Cl2], and [ICl], must be in units of moles per liter (M).
Kp = Kc*(RT)^delta n where
dn = nproducts-nreactants
Substitute and solve for Kc.