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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 [tex](n_{A}) = 1[/tex]

Mole ratio of the base, NaOH [tex](n_{B}) = 2[/tex]

Next, we shall determine the volume of NaOH required to react with H₂SO₄. This can be obtained as follow:

Molarity of the base, NaOH [tex](M_{B}) = 0.505 M[/tex]

Volume of the acid, H₂SO₄ [tex](V_{A}) = 40 mL[/tex]

Molarity of the acid, H₂SO₄ [tex](M_{A}) = 0.505 M[/tex]

Volume of the base, NaOH [tex](V_{B})[/tex] =?

[tex]\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}[/tex]

Cross multiply

[tex]0.505 * V_{B} = 20.2 * 2\\0.505 * V_{B} = 40.4[/tex]

Divide both side by 0.505

[tex]V_{B} = \frac{40.4}{0.505}\\\\V_{B} = 80 mL[/tex]

Finally, we shall convert 80 mL to dm³. This can be obtained as follow:

[tex]1000 mL = 1 dm^{3}\\\\Therefore,\\\\80 mL = \frac{80 mL * 1dm^{3}}{1000 mL}\\\\80 mL = 0.08dm^{3}[/tex]

Therefore, the volume of NaOH required is 0.08 dm³

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