The equilibrium constant for a reaction was measured at several temperatures and the data plotted at right. The slope and y-intercept of the plot are +3.25 kK and -4.04, respectively. Calculate ΔrH(std), ΔrS(std), and ΔrG(std) using this

information.

To calculate the standard enthalpy change (ΔrH(std)), we can use the Van't Hoff equation, which relates the equilibrium constant (K) to the standard enthalpy change:

ln(K2/K1) = (-ΔrH(std)/R) * (1/T2 - 1/T1)

Where K1 and T1 are the initial equilibrium constant and temperature, and K2 and T2 are the final equilibrium constant and temperature.

Given that the slope of the plot is +3.25 kK, which represents ΔrH(std)/R, we can rearrange the equation to solve for ΔrH(std):

ΔrH(std) = slope * R

Using the gas constant, R = 8.314 J/(mol·K), we can calculate ΔrH(std):

ΔrH(std) = 3.25 kK * 8.314 J/(mol·K)
ΔrH(std) = 26.97 kJ/mol

Therefore, the standard enthalpy change (ΔrH(std)) is 26.97 kJ/mol.

To calculate the standard entropy change (ΔrS(std)), we can use the equation:

ΔrG(std) = ΔrH(std) - T * ΔrS(std)

Given that the y-intercept of the plot is -4.04, which represents ΔrG(std) at standard conditions (ΔrG(std) = 0), we can rearrange the equation to solve for ΔrS(std):

ΔrS(std) = ΔrH(std)/T - ΔrG(std)/T

Since ΔrG(std) = 0 at standard conditions, the equation simplifies to:

ΔrS(std) = ΔrH(std)/T

Using the slope (ΔrH(std))/R = 3.25 kK and the gas constant R = 8.314 J/(mol·K), we can rearrange the equation to solve for ΔrS(std):

ΔrS(std) = (slope * R)/T

Using the value for T at which the equilibrium constant is measured, we can calculate ΔrS(std). Unfortunately, the temperature information is not provided, so it is not possible to provide an exact value for ΔrS(std) without that information.

To calculate ΔrH(std), ΔrS(std), and ΔrG(std) using the given information, we can use the Van't Hoff equation:

ΔrG(std) = -RTlnK

Where:
ΔrG(std) is the standard change in Gibbs free energy of the reaction
R is the gas constant (8.314 J/(mol·K))
T is the absolute temperature in Kelvin
K is the equilibrium constant

First, we need to calculate the enthalpy change (ΔrH(std)) and entropy change (ΔrS(std)) using the slope and intercept of the plot.

The slope of the plot (+3.25 kK) represents ΔrH(std) divided by -R:

slope = ΔrH(std) / -R

ΔrH(std) = slope * -R

ΔrH(std) = (3.25 kK) * (-8.314 J/(mol·K))

Note: We convert 3.25 kK to kelvin by multiplying it by 1000.

Next, the y-intercept (-4.04) represents -ΔrG(std)/R:

y-intercept = -ΔrG(std)/R

ΔrG(std) = -y-intercept * R

ΔrG(std) = (-4.04) * (8.314 J/(mol·K))

Now, ΔrS(std) can be calculated using the equation:

ΔrS(std) = ΔrG(std) / T

where T is the temperature in Kelvin. Since the equation will be used in the Van't Hoff equation, we use the intermediate value of T.

To calculate the final values, you need to convert the units and do the calculations with the specific values provided.