Question #8818a
1 Answer
Here's what I got.
Explanation:
The idea here is that you're required to calculate the volume of water that would be needed in order to dilute the hydrochloric acid solution, i.e. to decrease the concentration of hydronium cations.
As you know, the concentration of hydronium cations is given by
#color(blue)(ul(color(black)(["H"_3"O"^(+)] = 10^(-"pH"))))#
The initial solution has a
#["H"_ 3"O"^(+)]_ 0 = 10^(-0.7) quad "M"#
This means that the
#14 color(red)(cancel(color(black)("L solution"))) * (10^(-0.7) quad "moles H"_3"O"^(+))/(1color(red)(cancel(color(black)("L solution")))) = "2.7934 moles H"_3"O"^(+)#
Now, when you dilute this solution, the number of moles of hydronium cations remains unchanged.
The target solution must have a
#["H"_ 3"O"^(+)]_ "fin" = 10^(-2.3) quad "M"#
If you take
#V = (2.7934 color(red)(cancel(color(black)("moles H"_3"O"^(+)))))/(10^(-2.3) color(red)(cancel(color(black)("moles H"_3"O"^(+)))) "L"^(-1)) = "557.4 L"#
So, you know that in order to decrease the
This means that the initial solution must be added to a volume of water equal to--remember, you must always add strong acids to water, never the other way around!
#V_"water" = "557.4 L " - " 14 L" = color(darkgreen)(ul(color(black)("540 L")))#
I'll leave the answer rounded to two sig figs, no decimal places, but keep in mind that one decimal place for the
So the volume of the target solution should be rounded to one significant figure
#"557.4 L " ~~ " 600 L"#
Now, because you have one more operation to perform, you can leave the volume of the solution as
Perform the subtraction normally
#"557.4 L " - " 14 L" = "543 L"#
and round the final answer to
#"543 L " ~~ " 500 L"#
This is actually a great example of how significant figures can affect the final answer.