What volume of \( 0.250 \mathrm{M} \mathrm{HNO}_{3} \) (nitric acid) reacts with 42.4 mL of \( 0.150 \mathrm{M}_{2} \mathrm{CO}_{3} \) (sodium carbonate) in the follow- ing reaction? \( 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \longrightarrow \) \( 2 \mathrm{NaNO}_{3}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g) \)

To find the volume of \( 0.250 \, \mathrm{M} \, \mathrm{HNO}_3 \) that reacts with \( 42.4 \, \mathrm{mL} \) of \( 0.150 \, \mathrm{M} \, \mathrm{Na}_2\mathrm{CO}_3 \), we first determine the moles of sodium carbonate: \[ \text{Moles of } \mathrm{Na}_2\mathrm{CO}_3 = \text{Volume (L)} \times \text{Molarity} = 0.0424 \, \mathrm{L} \times 0.150 \, \mathrm{mol/L} = 0.00636 \, \text{mol} \] The balanced equation shows that \( 2 \, \mathrm{HNO}_3 \) reacts with \( 1 \, \mathrm{Na}_2\mathrm{CO}_3 \). Thus, the moles of \( \mathrm{HNO}_3 \) required are: \[ \text{Moles of } \mathrm{HNO}_3 = 2 \times 0.00636 \, \text{mol} = 0.01272 \, \text{mol} \] Next, we calculate the volume of \( 0.250 \, \mathrm{M} \, \mathrm{HNO}_3 \): \[ \text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.01272 \, \text{mol}}{0.250 \, \text{mol/L}} = 0.05088 \, \text{L} = 50.88 \, \mathrm{mL} \] So, the volume of \( 0.250 \, \mathrm{M} \, \mathrm{HNO}_3 \) required is approximately \( 50.9 \, \mathrm{mL} \). Historical Background: Did you know that nitric acid has been used since ancient times? The alchemists were some of the first to discover its powerful properties. They called it "aqua fortis," or "strong water," because of its ability to dissolve metals. Its discovery laid the groundwork for modern chemistry and the synthesis of various compounds! Real-World Application: Nitric acid is quite the multitasker in the real world! It's used not only in laboratories but also in the production of fertilizers and explosives. In the automotive industry, it's a key ingredient in creating nitro compounds used in high-performance fuels. So, when you're speeding down the track in a race car, just know that nitric acid played a vital role in your fuel's performance!