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What volume of 11.0 M acid is required to make 1 dm³ of 0.05 M acid?

Chemistry

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Step-by-step solution

5 steps
  1. Identify the given values for the concentrated and diluted solutions.

    Concentrated acid:
    Initial concentration (M1M_1) = 11.0 M11.0 \text{ M}
    Initial volume (V1V_1) = ?

    Diluted acid:
    Final concentration (M2M_2) = 0.05 M0.05 \text{ M}
    Final volume (V2V_2) = 1 dm31 \text{ dm}^3

  2. Convert the final volume to cm3\text{cm}^3 to match the units in the options.

    We know that 1 dm3=1000 cm31 \text{ dm}^3 = 1000 \text{ cm}^3.
    So, V2=1000 cm3V_2 = 1000 \text{ cm}^3.

  3. Use the dilution formula.

    The dilution formula states that the number of moles of solute remains constant before and after dilution:

    M1V1=M2V2M_1V_1 = M_2V_2
  4. Substitute the known values into the formula and solve for V1V_1.

    11.0 M×V1=0.05 M×1000 cm311.0 \text{ M} \times V_1 = 0.05 \text{ M} \times 1000 \text{ cm}^3 V1=0.05 M×1000 cm311.0 MV_1 = \frac{0.05 \text{ M} \times 1000 \text{ cm}^3}{11.0 \text{ M}} V1=50 cm311.0V_1 = \frac{50 \text{ cm}^3}{11.0} V1≈4.545 cm3V_1 \approx 4.545 \text{ cm}^3
  5. Compare the calculated volume with the given options.

    The calculated volume is approximately 4.55 cm34.55 \text{ cm}^3.
    The options are:
    A. 5 cm35 \text{ cm}^3
    B. (partially visible)
    C. 550 cm3550 \text{ cm}^3
    D. 11000 cm311000 \text{ cm}^3

    Option A, 5 cm35 \text{ cm}^3, is the closest value to the calculated 4.55 cm34.55 \text{ cm}^3.

    The final answer is A. 5cm3\boxed{\text{A. 5cm}^3}.

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