For a chemical reaction, a graph is plotted between the natural logarithm of the rate constant ( k ) and the inverse of temperature ( 1 T ). If the resulting plot is a straight line, the activation energy ( E_a ) for the reaction can be calculated using which of the following expressions? (where R is the universal gas constant)

Step-by-step solution

According to the Arrhenius equation: k = A e^ -E_a/RT Taking the natural logarithm on both sides gives: k = A - E_a RT This equation is in the form of a straight line, y = mx + c , where y = k and x = 1 T . The slope of this line ( m ) is equal to - E_a R . Therefore, the activation energy can be calculated as: E_a = - slope R Using - 2.303 slope R is a common mistake when confusing the plot of k versus 1/T with the plot of k versus 1/T . Answer: - slope R