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Determine the moles of CaCO3 used given the volume of CO2 produced in Experiment A and the molar gas volume at 40°C.

Chemistry

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Answer

1.79 g\text{1.79 g}

Step-by-step solution

5 steps
  1. Determine the total volume of CO2_2 produced.

    From the graph, the reaction for Experiment A stops at a maximum volume of CO2_2 gas.

    Volume of CO2=460 cm3\text{Volume of CO}_2 = 460 \text{ cm}^3
  2. Convert the volume of CO2_2 to dm3^3.

    Since the molar gas volume is given in dm^3$$\cdotmol−1^{-1}, convert the volume of CO2_2 from cm3^3 to dm3^3.

    1 dm3=1000 cm31 \text{ dm}^3 = 1000 \text{ cm}^3 Volume of CO2=4601000 dm3=0.460 dm3\text{Volume of CO}_2 = \frac{460}{1000} \text{ dm}^3 = 0.460 \text{ dm}^3

    Step 3: Calculate the moles of CO2_2 produced.
    Use the given molar gas volume at 40°C, which is 25.7 dm^3$$\cdotmol−1^{-1}.

    Moles of CO2=Volume of CO2Molar gas volume\text{Moles of CO}_2 = \frac{\text{Volume of CO}_2}{\text{Molar gas volume}} Moles of CO2=0.460 dm325.7 dm3⋅mol−1\text{Moles of CO}_2 = \frac{0.460 \text{ dm}^3}{25.7 \text{ dm}^3\cdot\text{mol}^{-1}} Moles of CO2≈0.0178988 mol\text{Moles of CO}_2 \approx 0.0178988 \text{ mol}
  3. Determine the moles of CaCO3_3 used.

    From the balanced chemical equation:

    CaCO3(s)+2HCl(aq)→CaCl2(aq)+H2O(l)+CO2(g)\text{CaCO}_3(\text{s}) + 2\text{HCl}(\text{aq}) \rightarrow \text{CaCl}_2(\text{aq}) + \text{H}_2\text{O}(\text{l}) + \text{CO}_2(\text{g})

    The mole ratio of CaCO3_3 to CO2_2 is 1:1.
    Therefore, moles of CaCO3_3 used = moles of CO2_2 produced.

    Moles of CaCO3=0.0178988 mol\text{Moles of CaCO}_3 = 0.0178988 \text{ mol}
  4. Calculate the molar mass of CaCO3_3.

    Molar mass of Ca = 40.08 g/mol
    Molar mass of C = 12.01 g/mol
    Molar mass of O = 16.00 g/mol

    Molar mass of CaCO3=40.08+12.01+(3×16.00)\text{Molar mass of CaCO}_3 = 40.08 + 12.01 + (3 \times 16.00) Molar mass of CaCO3=40.08+12.01+48.00=100.09 g/mol\text{Molar mass of CaCO}_3 = 40.08 + 12.01 + 48.00 = 100.09 \text{ g/mol}
  5. Calculate the mass of CaCO3_3 used.

    Mass of CaCO3=Moles of CaCO3×Molar mass of CaCO3\text{Mass of CaCO}_3 = \text{Moles of CaCO}_3 \times \text{Molar mass of CaCO}_3 Mass of CaCO3=0.0178988 mol×100.09 g/mol\text{Mass of CaCO}_3 = 0.0178988 \text{ mol} \times 100.09 \text{ g/mol} Mass of CaCO3≈1.7915 g\text{Mass of CaCO}_3 \approx 1.7915 \text{ g}

    Rounding to two decimal places:

    Mass of CaCO3≈1.79 g\text{Mass of CaCO}_3 \approx 1.79 \text{ g}

    The mass of CaCO3_3(s) used in experiment A is 1.79 g\boxed{\text{1.79 g}}.

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