The volume of NaOH required is 0.08 dm³
To solve this question, we'll begin by writing the balanced equation for the reaction between H₂SO₄ and NaOH. This is illustrated below:
H₂SO₄ + 2NaOH —> Na₂SO₄ + 2H₂O
From the balanced equation above,
Mole ratio of the acid, H₂SO₄
Mole ratio of the base, NaOH ![(n_{B}) = 2](https://tex.z-dn.net/?f=%28n_%7BB%7D%29%20%3D%202)
Next, we shall determine the volume of NaOH required to react with H₂SO₄. This can be obtained as follow:
Molarity of the base, NaOH ![(M_{B}) = 0.505 M](https://tex.z-dn.net/?f=%28M_%7BB%7D%29%20%3D%200.505%20M)
Volume of the acid, H₂SO₄ ![(V_{A}) = 40 mL](https://tex.z-dn.net/?f=%28V_%7BA%7D%29%20%3D%2040%20mL)
Molarity of the acid, H₂SO₄ ![(M_{A}) = 0.505 M](https://tex.z-dn.net/?f=%28M_%7BA%7D%29%20%3D%200.505%20M)
<h3>Volume of the base, NaOH
![(V_{B})](https://tex.z-dn.net/?f=%28V_%7BB%7D%29)
=? </h3>
![\frac{M_{A} * V_{A}}{M_{B} * V_{B}} = \frac{n_{A}}{n_{B}}\\\\\frac{0.505 * 40}{0.505 *V_{B}} = \frac{1}{2}\\\\\frac{20.2}{0.505 *V_{B}} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BM_%7BA%7D%20%2A%20V_%7BA%7D%7D%7BM_%7BB%7D%20%2A%20V_%7BB%7D%7D%20%3D%20%5Cfrac%7Bn_%7BA%7D%7D%7Bn_%7BB%7D%7D%5C%5C%5C%5C%5Cfrac%7B0.505%20%2A%2040%7D%7B0.505%20%2AV_%7BB%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7B20.2%7D%7B0.505%20%2AV_%7BB%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Cross multiply
![0.505 * V_{B} = 20.2 * 2\\0.505 * V_{B} = 40.4](https://tex.z-dn.net/?f=0.505%20%2A%20V_%7BB%7D%20%3D%2020.2%20%2A%202%5C%5C0.505%20%2A%20V_%7BB%7D%20%3D%2040.4)
Divide both side by 0.505
![V_{B} = \frac{40.4}{0.505}\\\\V_{B} = 80 mL](https://tex.z-dn.net/?f=V_%7BB%7D%20%3D%20%5Cfrac%7B40.4%7D%7B0.505%7D%5C%5C%5C%5CV_%7BB%7D%20%3D%2080%20mL)
Finally, we shall convert 80 mL to dm³. This can be obtained as follow:
![1000 mL = 1 dm^{3}\\\\Therefore,\\\\80 mL = \frac{80 mL * 1dm^{3}}{1000 mL}\\\\80 mL = 0.08dm^{3}](https://tex.z-dn.net/?f=1000%20mL%20%3D%201%20dm%5E%7B3%7D%5C%5C%5C%5CTherefore%2C%5C%5C%5C%5C80%20mL%20%3D%20%5Cfrac%7B80%20mL%20%2A%201dm%5E%7B3%7D%7D%7B1000%20mL%7D%5C%5C%5C%5C80%20mL%20%3D%200.08dm%5E%7B3%7D)
Therefore, the volume of NaOH required is 0.08 dm³
Learn more: brainly.com/question/19053582