Exponential and Logarithmic Model

Question

The acidity of a solution is measured on a pH scale with pH = −log[H+] where H+ is the hydrogen ion concentration of the solution (in moles per liter).

How many times more hydrogen ion concentration does lemon juice have compared to that of rainwater given that lemon juice has a pH of 2.0 while rainwater has a pH of 6.5 ? Round answer to the nearest whole number.

lemon juice has (  )  times more hydrogen ion concentration than rainwater

Answer 1

To solve this problem first you need to calculate the concentration of the H+ ion for each substance.

You will need to use the following log identity

y=log_bx --> b^y=x

Lemon Juice

pH = −log[H+] Formula for PH

2 = - log[H+]_lemon

-2 = log[H+]_{lemon This is log base 10}

10^(-2)= [H+]_lemon

0.01 =[H+]_lemon

Rain Water

pH = −log[H+] Formula for PH

6.5 = - log[H+]_water

-6.5 = log[H+]_water

10^(-6.5)= [H+]_water

3.16x10^-7 =[H+]_water

Now we can determine how many times more H+ concentration in the lemon juice compare with rain water

Lemon Juice [H+] ÷ Rain water [H+]

0.01 ÷ 3.16x10^-7= 31646

Hope this helps