A student in lab gathered temperature and concentration data for the solubility of borax and generated a plot of ln(Ksp) vs. 1/T having the equation of the line y = -11655x + 35.585. Determine the temperature (in units of K) at which the reaction becomes spontaneous.

To determine the temperature at which the reaction becomes spontaneous, we need to find the point on the plot where the ln(Ksp) value is zero. This corresponds to the point on the line y = -11655x + 35.585 where y = 0.

Let's set y = 0 in the equation y = -11655x + 35.585:

0 = -11655x + 35.585

Solving for x, we get:

11655x = 35.585

x = 35.585 / 11655

x ≈ 0.0031

Now that we have the value of x, we can determine the value of 1/T by substituting x into the equation 1/T = x:

1/T = 0.0031

Rearranging the equation, we get:

T = 1 / 0.0031

T ≈ 322.5806

Therefore, the temperature at which the reaction becomes spontaneous is approximately 322.5806 K.