what mass of sodium hydroxide has the same number of oxygen atoms as 130g of barium dihydrogen phosphate

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what mass of sodium hydroxide has the same number of oxygen atoms as 130g of barium dihydrogen phosphate

The Correct Answer and Explanation is:

Step 1: Determine the number of oxygen atoms in 130 g of Ba(H₂PO₄)₂

  1. Molar mass of Ba(H₂PO₄)₂:
    • Ba = 137.33 g/mol
    • H = 1.008 × 4 = 4.032 g/mol
    • P = 30.97 × 2 = 61.94 g/mol
    • O = 16.00 × 8 = 128.00 g/mol
    • Total molar mass = 137.33 + 4.032 + 61.94 + 128.00 = 331.30 g/mol
  2. Moles of Ba(H₂PO₄)₂ in 130 g: Moles=130331.30≈0.3924 mol\text{Moles} = \frac{130}{331.30} \approx 0.3924 \text{ mol}Moles=331.30130​≈0.3924 mol
  3. Oxygen atoms per formula unit of Ba(H₂PO₄)₂:
    Each H₂PO₄⁻ group has 4 oxygen atoms. There are 2 such groups, so: Total O atoms per molecule=4×2=8\text{Total O atoms per molecule} = 4 × 2 = 8Total O atoms per molecule=4×2=8
  4. Total moles of oxygen atoms: 0.3924 mol×8=3.139 mol O atoms0.3924 \text{ mol} × 8 = 3.139 \text{ mol O atoms}0.3924 mol×8=3.139 mol O atoms

Step 2: Determine the mass of NaOH that contains 3.139 mol of oxygen atoms

  1. Each NaOH contains 1 oxygen atom
    Therefore, 1 mol of NaOH provides 1 mol of oxygen atoms.
  2. We need 3.139 mol of NaOH to get 3.139 mol of O atoms
  3. Molar mass of NaOH:
    Na = 22.99 g/mol
    O = 16.00 g/mol
    H = 1.008 g/mol
    Total = 22.99 + 16.00 + 1.008 = 39.998 g/mol
  4. Mass of NaOH: Mass=3.139 mol×39.998 g/mol≈125.54 g\text{Mass} = 3.139 \text{ mol} × 39.998 \text{ g/mol} \approx \boxed{125.54 \text{ g}}Mass=3.139 mol×39.998 g/mol≈125.54 g​

Final Answer:

125.54 grams of sodium hydroxide contain the same number of oxygen atoms as 130 grams of barium dihydrogen phosphate.

Textbook-Style Explanation:

To compare the number of oxygen atoms in two substances, one must consider both the chemical formulas and the quantities involved. Barium dihydrogen phosphate, Ba(H₂PO₄)₂, contains two dihydrogen phosphate groups, each contributing four oxygen atoms, for a total of eight per formula unit. By calculating the number of moles in the given mass and multiplying by the number of oxygen atoms per mole, we determine the total moles of oxygen atoms.

Sodium hydroxide, NaOH, contains only one oxygen atom per molecule. Therefore, the number of moles of NaOH needed equals the number of moles of oxygen atoms required. By multiplying the required moles of NaOH by its molar mass, we find the mass necessary to match the oxygen content of the original compound.

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