A student combines 364.6 g of HCl with 80 g of NaOH in 5 L of water. What additional volume of H2O must be added to this mixture to yield a solution with a pH of 1? Note that the molar mass of HCl is 35.46 g/mole, while that of NaOH is 40 g/mole.

75L of additional water to have a pH 1 solution

Explanation:

The reaction of HCl With NaOH is:

HCl + NaOH → H₂O + NaCl

By using molar mass of each reactant you can know how many moles will react, thus:

HCl: 364.6g HCl ₓ (1mol / 36.46g) = 10 moles HCl

NaOH: 80g NaOH ₓ (1mol / 40g) = 2 moles NaOH

That means after the reaction will remain in solution, 10-2 = 8 moles of HCl = 8 moles of H⁺ (In water, HCl dissociates as H⁺ and Cl⁻ ions).

A solution with pH = 1 contains:

pH = -log [H⁺]

1 = -log [H⁺]

0.1M = [H⁺]

As molarity, M is the ratio between moles and liters and you want a solution 0.1M having 8 moles of H⁺ you require:

0.1M = 8 moles H⁺ / 80L

As the student combines the solution with 5L of water, you require

in scientific notation, the value of the  speed of light in a vacuum

  will be written as 2.995 * 10^8. when this value is represented in the form of

  a * 10^b, then, a = 2.995 and b = 8.

the value of the speed of light in a vacuum given above can also be rounded up to approximately 300000000. in this case, the scientific notation will be written as 3 *10^8.