Math Problem Statement

Solve using GRESA METHOD

How much 0.80 M HCl would be needed to dissolve a CaCO₃ pearl which weighs 34.0 grams?

Solution

The GRESA method stands for:

  • Given
  • Required
  • Equation
  • Solution
  • Answer

Let's apply this method to solve the problem:

1. GIVEN:

  • Chemical reaction:
    CaCO3+2HClCaCl2+H2O+CO2CaCO_3 + 2HCl \rightarrow CaCl_2 + H_2O + CO_2
  • Mass of CaCO₃ = 34.0 g
  • HCl concentration = 0.80 M

2. REQUIRED:

Find the volume of 0.80 M HCl needed to dissolve the given amount of CaCO₃.

3. EQUATION:

We need to use the concept of stoichiometry to determine the amount of HCl required.

  1. Calculate moles of CaCO₃ using its molar mass:
    Molar mass of CaCO3=40.08+12.01+(3×16.00)=100.09 g/molMolar\ mass\ of\ CaCO_3 = 40.08 + 12.01 + (3 \times 16.00) = 100.09\ g/mol
    Moles of CaCO3=MassMolar Mass=34.0 g100.09 g/mol\text{Moles of } CaCO_3 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{34.0\ g}{100.09\ g/mol}
    =0.34 mol= 0.34\ mol

  2. Use the balanced equation to find moles of HCl needed:

    • From the equation: 1 mol of CaCO₃ reacts with 2 mol of HCl
    • So, 0.34 mol of CaCO₃ reacts with:
      0.34×2=0.68 mol of HCl0.34 \times 2 = 0.68\ mol\ of\ HCl
  3. Find the volume of HCl solution required using molarity formula:
    Molarity(M)=Moles of soluteVolume (L)Molarity (M) = \frac{\text{Moles of solute}}{\text{Volume (L)}}
    Volume=Moles of HClMolarityVolume = \frac{\text{Moles of HCl}}{\text{Molarity}}
    =0.68 mol0.80 mol/L= \frac{0.68\ mol}{0.80\ mol/L}
    =0.85 L=850 mL= 0.85\ L = 850\ mL

4. SOLUTION:

By following the stoichiometric steps, we determined that the volume of 0.80 M HCl required to dissolve 34.0 g of CaCO₃ is 850 mL.

5. ANSWER:

850 mL of 0.80 M HCl is needed to dissolve a 34.0 g CaCO₃ pearl.


Would you like a more detailed explanation for any step?

Related Questions:

  1. What volume of 1.00 M HCl would be needed instead?
  2. How much CO₂ gas is produced in this reaction?
  3. What happens if an excess of HCl is added?
  4. How would the required volume of HCl change if 17 g of CaCO₃ were used?
  5. How does temperature affect the reaction rate?

Tip:

Always check the balanced chemical equation before performing stoichiometric calculations!

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Math Problem Analysis

Mathematical Concepts

Stoichiometry
Molarity
Moles of substances
Chemical equations

Formulas

Molarity (M) = Moles of solute / Volume (L)
Moles = Mass / Molar Mass

Theorems

Stoichiometry
Balanced chemical equation

Suitable Grade Level

Grades 9-12