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Balance the chemical equation: wH2SO4 + xAl(OH)3 -> yH2O + zAl2(SO4)3

Chemistry

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Answer

D\text{D}

Step-by-step solution

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To balance the chemical equation wH2SO4+xAl(OH)3→yH2O+zAl2(SO4)3w\text{H}_2\text{SO}_4 + x\text{Al}(\text{OH})_3 \rightarrow y\text{H}_2\text{O} + z\text{Al}_2(\text{SO}_4)_3, we need to ensure that the number of atoms of each element is the same on both sides of the equation.

  1. Balance the Aluminum (Al) atoms.

    On the reactant side, there are xx Al atoms in xAl(OH)3x\text{Al}(\text{OH})_3.
    On the product side, there are 2z2z Al atoms in zAl2(SO4)3z\text{Al}_2(\text{SO}_4)_3.
    So, x=2zx = 2z.

  2. Balance the Sulfate (SO4\text{SO}_4) groups.

    On the reactant side, there are ww SO4\text{SO}_4 groups in wH2SO4w\text{H}_2\text{SO}_4.
    On the product side, there are 3z3z SO4\text{SO}_4 groups in zAl2(SO4)3z\text{Al}_2(\text{SO}_4)_3.
    So, w=3zw = 3z.

  3. Assign a value to zz to find initial coefficients.

    Let's assume z=1z = 1 (the simplest whole number).
    Then, from Step 1: x=2×1=2x = 2 \times 1 = 2.
    And from Step 2: w=3×1=3w = 3 \times 1 = 3.

  4. Substitute the values of w,x,zw, x, z into the equation and balance Hydrogen (H) and Oxygen (O) atoms to find yy.

    The equation becomes:
    3H2SO4+2Al(OH)3→yH2O+1Al2(SO4)33\text{H}_2\text{SO}_4 + 2\text{Al}(\text{OH})_3 \rightarrow y\text{H}_2\text{O} + 1\text{Al}_2(\text{SO}_4)_3

    Count H atoms on the reactant side:
    From 3H2SO43\text{H}_2\text{SO}_4: 3×2=63 \times 2 = 6 H atoms.
    From 2Al(OH)32\text{Al}(\text{OH})_3: 2×3=62 \times 3 = 6 H atoms.
    Total H atoms on reactant side = 6+6=126 + 6 = 12.

    Count H atoms on the product side:
    From yH2Oy\text{H}_2\text{O}: y×2=2yy \times 2 = 2y H atoms.
    Equating H atoms: 12=2y⇒y=612 = 2y \Rightarrow y = 6.

  5. Verify the balance of Oxygen (O) atoms.

    Count O atoms on the reactant side:
    From 3H2SO43\text{H}_2\text{SO}_4: 3×4=123 \times 4 = 12 O atoms.
    From 2Al(OH)32\text{Al}(\text{OH})_3: 2×3=62 \times 3 = 6 O atoms.
    Total O atoms on reactant side = 12+6=1812 + 6 = 18.

    Count O atoms on the product side:
    From yH2Oy\text{H}_2\text{O} (with y=6y=6): 6×1=66 \times 1 = 6 O atoms.
    From 1Al2(SO4)31\text{Al}_2(\text{SO}_4)_3: 1×(4×3)=121 \times (4 \times 3) = 12 O atoms.
    Total O atoms on product side = 6+12=186 + 12 = 18.
    The oxygen atoms are balanced.

  6. State the final coefficients.

    The respective values for $w, x, y, z$ are $3, 2, 6, 1$.

  7. Compare with the given options.

    A: 2,2,6 and 2
    B: 2,2,5 and 1
    C: 3,2,5 and 2
    D: 3,2,6 and 1

    The calculated values match option D.

    The final answer is D\text{D}.

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