acetylsalicylic acid (aspirin) HC9H7O4 is the most widely used pain reliever and fever reducer. Find the PH of 0.040 M aqueous aspirin at body temperature (Ka at 37 C = 3.6 x 10-4)
is this correct?
initial concentration is 0.040 M. let change in concentration to equilibrium equal "x". thus, equilibrium concentration of HC9H7O4 is 0.040-x, cause aspirin is a reactant so it decreases in the reaction. thus, "x" amount C9H7O4- (conjugate base) is present at equilibium. so is "x" amount of H+.
Ka for this reaction is ([C9H7O4][H+])/[HC9H7O4]=3.6*10^-4. so substitute values.
Ka=([x][x])/0.040-x=3.6*10^-4. the -x in the denominator is negligible, as the power of Ka is less than 10^-3
so you have x^2/0.040=3.6*10^-4
so x^2=14.4*10^-6. take square root of both sides and x is 3.79 *10^-3
X is the concentration or molarity of H+ ions at equilibrium. pH = -log (3.79 *10^-3)=2.42
Yes, your calculations are correct. To find the pH of a 0.040 M aqueous solution of aspirin at body temperature, you need to use the equilibrium expression for the dissociation of aspirin, HC9H7O4.
Here's a step-by-step explanation of how you arrived at the answer:
1. Start with the initial concentration of aspirin, which is 0.040 M.
2. Let the change in concentration to equilibrium be represented by "x". The equilibrium concentration of HC9H7O4 is then 0.040 - x because aspirin is a reactant and decreases in the reaction.
3. The conjugate base of aspirin, C9H7O4-, is also present at equilibrium in the amount of "x".
4. Since the reaction is in equilibrium, the equilibrium expression for the acid dissociation reaction is given by Ka = [C9H7O4-][H+]/[HC9H7O4].
5. Substitute the values in the equation: Ka = [x][x]/(0.040 - x).
6. Neglect the value of -x in the denominator because the power of Ka is less than 10^-3.
7. Simplify the equation: x^2/(0.040) = 3.6 * 10^-4.
8. Multiply both sides of the equation by 0.040 to get x^2 = 14.4 * 10^-6.
9. Take the square root of both sides of the equation to find x, which is the concentration or molarity of H+ ions at equilibrium. You get x = 3.79 * 10^-3.
10. Finally, calculate the pH using the formula pH = -log[H+]. Substitute the value of x into the equation: pH = -log(3.79 * 10^-3) = 2.42.
Therefore, the pH of a 0.040 M aqueous solution of aspirin at body temperature is 2.42.