What is the pH of a solution containing 200 mg of H+ (mass = 2 amu) in 1 kL of solution?

Question

  pH = 1

 

  pH = 4

 

  pH = 6

 

  pH = 2

 

Answer 1

pH is equal to the negative logarithm of the concentration of H+, we write that like this (the brackets mean concentration):

pH=-log([H+])

Concentration should be measured in moles of hydrogen ion per Liter. We're given mg of hydrogen ion instead of moles and kL instead of Liters, so we'll convert both of those to the proper units.

We can convert mg of hydrogen ion to moles by first converting to grams: 200mg (given) is equal to 0.2 grams. Then, we can convert from grams to moles by using Hydrogen's molar mass. The molar mass of hydrogen ion is typically 1 amu, but it's given in the problem as 2 amu, which would be true for an uncommon isotope of hydrogen ion. Using the given molar mass of 2 amu (which is the same as 2 grams/mole), we can do 0.2 grams multiplied by 1 mole/2 grams to get 0.1 moles of hydrogen ion. Notice that we flipped the 2grams/mole to 1 mole/2grams in order to cancel out grams when we multiplied.

Using our SI units, 1 kL of solution is equal to 1000 Liters of solution.

Since concentration is measured in moles/Liter, we can now do 0.1moles H+/1000L of solution to get 1*10^-4 M H+. The capital M stands for Molarity which is just a faster way to say Moles/L.

Plugging this into our formula for pH gives this:

pH=-log(1*10^-4)

pH=4

Hope this helps!