Question

95. Because atoms, molecules, and ions are very small, they are counted in units of moles, where 1 mole = 6.022 × 1023 molecules. Concentration of ions in a liquid is measured in units of moles per liter. The measure of the acidity of a liquid is called the pH of the liquid and is given by the formula
pH = −log(H),
where H is the concentration of hydrogen ions in units of moles per liter.
a. Water has a pH value of 7.0. How many hydrogen ions are in one liter of water?

Answer 1

Answer:

There are 10⁻⁷ hydrogen ions in one-liter water

Step-by-step explanation:

Hi there!

a. If the pH = 7.0, then:

-log(H) = 7.0

multiply both sides of the equation  by -1

log(H) = -7.0

Apply 10ˣ to both sides

10^(log (H)) = 10⁻⁷

(H) = 10⁻⁷

There are 10⁻⁷ hydrogen ions in one-liter water.

Why 10^(log (H)) = (H)?

Let´s consider this function:

y = 10^(log x)

(Apply log to both sides)

log y = log 10^(log x)

(Apply logarithmic property: log xᵃ = a · log x)

log y = log x · log 10

(log 10 = 1)

log y = log x

y = x

(since y =  10^(log x) and y = x):

10^(log x) = x

That´s why 10^(log (H)) = (H)