80 g of sodium hydroxide reacts with excess sulfuric acid to produce 142 g of sodium sulfate. what mass of sodium hydroxide would be needed in order to make 50 g of sodium sulfate? give your answer to one decimal place

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80 g of sodium hydroxide reacts with excess sulfuric acid to produce 142 g of sodium sulfate. what mass of sodium hydroxide would be needed in order to make 50 g of sodium sulfate? give your answer to one decimal place.

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LectureNotes said 80 g of sodium hydroxide reacts with excess sulfuric acid to produce 142 g of sodium sulfate. What mass of sodium hydroxide would be needed in order to make 50 g of sodium sulfate? Give your answer to one decimal place.

To determine the mass of sodium hydroxide (NaOH) needed to produce 50 g of sodium sulfate (Na₂SO₄), we can use a simple proportion based on the given data. Here’s the step-by-step solution:

  1. Given Data:

    • 80 g of NaOH produces 142 g of Na₂SO₄.

  2. Set up the proportion:
    We need to find the mass of NaOH (( x )) that would produce 50 g of Na₂SO₄.

    \frac{80 \, \text{g NaOH}}{142 \, \text{g Na₂SO₄}} = \frac{x \, \text{g NaOH}}{50 \, \text{g Na₂SO₄}}

  3. Solve for ( x ):
    Cross-multiply to solve for ( x ):

80 \, \text{g NaOH} \times 50 \, \text{g Na₂SO₄} = 142 \, \text{g Na₂SO₄} \times x \, \text{g NaOH}

4000 = 142x

x = \frac{4000}{142}

x \approx 28.2 \, \text{g NaOH}

Therefore, the mass of sodium hydroxide needed to produce 50 g of sodium sulfate is approximately ( \boxed{28.2} ) grams.