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For the reaction 2A(g) + 3B(g) = C(g) Kc = 38.8 at a temperature of 51 °C. Calculate the value of Kp. Express your answer numerically. View Available Hint(s) VALO ?

Answer :

Final answer:

The value of Kp for the given reaction is 0.014.

Explanation:

To calculate the value of Kp from Kc, we need to use the ideal gas law and the relationship between partial pressure and concentration for gases.

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin. To do this, we add 273 to the given temperature:

T(K) = 51 + 273 = 324 K

Next, we need to determine the number of moles of each gas present in the reaction. From the balanced equation, we can see that 2 moles of A react with 3 moles of B to form 1 mole of C.

Since the stoichiometric coefficients are in a 2:3:1 ratio, we can assume that the initial concentrations of A, B, and C are in the same ratio.

Let's assume the initial concentration of A is x M. Then, the initial concentrations of B and C would be (3/2)x M and (1/2)x M, respectively.

Now, we can use the ideal gas law to calculate the partial pressures of A, B, and C:

PA = (x)(RT/V)

PB = ((3/2)x)(RT/V)

PC = ((1/2)x)(RT/V)

Since Kp is the ratio of the partial pressures of the products to the partial pressures of the reactants, we can express Kp as:

Kp = (PC / (PA^2 * PB^3))

Substituting the expressions for PA, PB, and PC, we get:

Kp = (((1/2)x)(RT/V)) / (((x)(RT/V))^2 * ((3/2)x)(RT/V))^3)

Simplifying the expression, we get:

Kp = (1/2) / (x^2 * (3/2)^3)

Finally, we can substitute the given value of Kc into the equation and solve for x:

38.8 = (1/2) / (x^2 * (3/2)^3)

Solving for x, we find:

x = 0.091 M

Therefore, the value of Kp is:

Kp = (1/2) / (0.091^2 * (3/2)^3) = 0.014

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Final answer:

The value of Kp for the given reaction is 0.014.

Explanation:

To calculate the value of Kp from Kc, we need to use the ideal gas law and the relationship between partial pressure and concentration for gases.

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin. To do this, we add 273 to the given temperature:

T(K) = 51 + 273 = 324 K

Next, we need to determine the number of moles of each gas present in the reaction. From the balanced equation, we can see that 2 moles of A react with 3 moles of B to form 1 mole of C.

Since the stoichiometric coefficients are in a 2:3:1 ratio, we can assume that the initial concentrations of A, B, and C are in the same ratio.

Let's assume the initial concentration of A is x M. Then, the initial concentrations of B and C would be (3/2)x M and (1/2)x M, respectively.

Now, we can use the ideal gas law to calculate the partial pressures of A, B, and C:

PA = (x)(RT/V)

PB = ((3/2)x)(RT/V)

PC = ((1/2)x)(RT/V)

Since Kp is the ratio of the partial pressures of the products to the partial pressures of the reactants, we can express Kp as:

Kp = (PC / (PA^2 * PB^3))

Substituting the expressions for PA, PB, and PC, we get:

Kp = (((1/2)x)(RT/V)) / (((x)(RT/V))^2 * ((3/2)x)(RT/V))^3)

Simplifying the expression, we get:

Kp = (1/2) / (x^2 * (3/2)^3)

Finally, we can substitute the given value of Kc into the equation and solve for x:

38.8 = (1/2) / (x^2 * (3/2)^3)

Solving for x, we find:

x = 0.091 M

Therefore, the value of Kp is:

Kp = (1/2) / (0.091^2 * (3/2)^3) = 0.014

Learn more about calculating kp from kc here:

https://brainly.com/question/31045446

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