Question

In experiments to determine the enthalpy of evaporation of propane, at different temperatures (T,K) enthalpy change values ​​(∆H, J/kmol) were determined. For the enthalpy of evaporation, equality is suggested. ∆ = ( − )^(/)

Here, A and n are the coefficients for propane, and Tc is the critical temperature.
Critical temperature of propane as it is known;
a) Make the equation linear,
b) Show how to determine the coefficients A and n on a rough graph.

Answer 1

To make the equation linear, a logarithmic transformation can be applied. Taking the natural logarithm of both sides of the equation will convert the power function into a linear form:

ln(∆H) = ln(A) + n * ln(Tc / T)

Now, the equation is linearized, and we can determine the coefficients A and n using a rough graph. Here's how you can do it:

a) Linearization:

Start by plotting a graph with ln(∆H) on the y-axis and ln(Tc / T) on the x-axis. Each data point (T, ∆H) from the experiments represents a point on the graph.

b) Determining coefficients A and n:

1. Find two points on the graph that are reasonably well-separated and lie on the linear portion. Ideally, these points should cover the entire range of the data.

2. Draw a straight line that best fits the data points.

3. Determine the slope of the straight line. The slope corresponds to the exponent 'n' in the original equation.

4. Determine the y-intercept of the straight line. The y-intercept corresponds to ln(A) in the original equation.

5. Calculate the value of 'A' by taking the exponential of the y-intercept.

A = e^(y-intercept)

By performing these steps and obtaining the values for the slope and y-intercept, you can determine the coefficients A and n for propane in the enthalpy of evaporation equation.