# Question 88580

Jul 7, 2017

$1 M$ ($1$ significant figure)

#### Explanation:

We're asked to find the molarity of the $\text{NaOH}$ solution given some titration values.

Let's first write the balanced chemical equation for this reaction:

$2 \text{NaOH"(aq) + "H"_2"SO"_4(aq) rarr "Na"_2"SO"_4 (aq) + 2"H"_2"O} \left(l\right)$

We can calculate the number of moles of ${\text{H"_2"SO}}_{4}$ used by using the molarity equation:

"mol solute" = ("molarity")("L soln")

We'll convert the volume to liters to use this equation:

"mol H"_2"SO"_4 = (0.5"mol"/(cancel("L")))(0.0205cancel("L")) = color(red)(0.0103 color(red)("mol H"_2"SO"_4

Using the coefficients of the chemical equation, we can determine thee relative number of moles of $\text{NaOH}$ used:

color(red)(0.0103)cancel(color(red)("mol H"_2"SO"_4))((2color(white)(l)"mol NaOH")/(1cancel("mol H"_2"SO"_4))) = 0.0205 $\text{mol NaOH}$

Lastly, we'll use the given volume of the $\text{NaOH}$ solution and the mole value to calculate the molarity of the solution:

$\text{molarity" = "mol solute"/"L soln}$

= (0.0205color(white)(l)"mol NaOH")/(0.020color(white)(l)"L") = color(blue)(1M#

which I'll leave to one significant figure I suppose (real value $= 1.025 M$).