Answer:
m = 3.4126 g
Step-by-step explanation:
First, the question is incomplete but I already put in the comments the rest of the question.
Let's solve the first two questions, and then the actual question you are asking here to give you a better explanation of how to do it.
1) We need the volume of the pool, in this case is easy. Assuming the pool is rectangular, we use the volume of a parallelepiped which is the following:
V = h * d * w
We have the data, but first we will convert the feet to centimeter. This is because is easier to work the volume in cm³ than in feet.
So the height, width and depth of the pool in centimeter are:
h = 32 * 30.48 = 975.36 cm
w = 18 * 30.48 = 548.64 cm
d = 5.3 * 30.48 = 161.54 cm
Now the volume:
V = 975.36 * 548.64 * 161.54
V = 86,443,528.79 cm³ or 86,443,528.79 mL or 86,443.5 L
2) If the pool has a pH of 6.4, the concentration of H+ can be calculated with the following expression:
[H+] = antlog(-pH) or 10^(-pH)
Replacing we have:
[H+] = 10^(-6.4)
[H+] = 3.98x10^-7 M
3) Finally the question you are asking for.
According to the reaction:
Na2CO3 + H+ → 2Na+ + HCO3−
We can see that there is ratio of 1:1 between the H+ and the Na2CO3, so, if we have initially a concentration of 3.98x10^-7 M, the difference between the new concentration of H+ and the innitial, will give the concentration to be added to the pool to raise the pH. Then, with the molecular weight of Na2CO3 (105.98 g/mol) we can know the mass needed.
The new concentration of [H+] is:
[H+] = 10^(-7.6) = 2.58x10^-8 M
The difference of both [H+] will give concentration of Na2CO3 used:
3.98x10^-7 - 2.58x10^-8 = 3.73x10^-7 M
The moles:
moles = 3.73x10^-7 * 86,443.5 = 0.0322 moles
Finally the mass:
m = 0.0322 * 105.98
m = 3.4126 g