When a student plotted ln [vapor pressure of a gas] vs. inverse Kelvin temperature, she obtained a straight line with a slope equal to -1.0500 x 10^4 K.

According to the Clausius Clapeyron equation, Hvap is
kJ/mol. ?

3 answers

The slope is -Hvap/R, so multiply the slope by R (the gas constant, in appropriate units) to get the heat pf vaporization, Hvap.

R = 8.317 J/mole K in case you have forgotten.
is the answer supposed to be 87297?
That depends upon the units you are using. Using the R value I gave you, the answer would be in Joules/mole. Always check and list dimensions

Divide by 1000 for kJ/mole

I get 87.33 kJ/mole. Maybe you used a slightly different R, with more significiant figures.