When surface water dissolves carbon dioxide, carbonic acid (H2CO3) is formed. When the water moves underground through limestone formations, the limestone dissolves and caves are sometimes produced.
CaCO3(s) + H2CO3(aq) Ca(HCO3)2(aq)
What mass of limestone must have dissolved if 4.93 1010 kg of calcium hydrogen carbonate was produced?
would the correct answer be 3.04e13??
i found this by taking 4.93e10kg converting it to grams= 4.93e13g Ca(HCO3)2 then converting that to moles and then setting that equal to limestone (CacCO3) and converting that then to grams.
triple post. See comments above.
To find the mass of limestone that dissolved, you need to use stoichiometry to convert the given mass of calcium hydrogen carbonate (Ca(HCO3)2) to the mass of limestone (CaCO3).
Let's break down the steps to solve the problem:
1. Convert the given mass of 4.93 x 10^10 kg of calcium hydrogen carbonate (Ca(HCO3)2) to grams:
4.93 x 10^10 kg = 4.93 x 10^13 g
2. Convert the mass of calcium hydrogen carbonate (Ca(HCO3)2) to moles:
To do this, you need to determine the molar mass of Ca(HCO3)2.
The molar mass of Ca(HCO3)2 can be calculated as follows:
1 calcium (Ca) atom = 1 x 40.08 g/mol = 40.08 g/mol
2 hydrogen (H) atoms = 2 x 1.01 g/mol = 2.02 g/mol
2 carbon (C) atoms = 2 x 12.01 g/mol = 24.02 g/mol
6 oxygen (O) atoms = 6 x 16.00 g/mol = 96.00 g/mol
Total molar mass = 40.08 + 2.02 + 24.02 + 96.00 = 162.12 g/mol
Now, divide the mass of calcium hydrogen carbonate (Ca(HCO3)2) in grams by the molar mass to get moles:
moles of Ca(HCO3)2 = (4.93 x 10^13 g) / (162.12 g/mol)
3. Use the stoichiometric ratio from the balanced equation to convert moles of Ca(HCO3)2 to moles of CaCO3:
From the balanced equation: 1 mole of Ca(HCO3)2 produces 1 mole of CaCO3
moles of CaCO3 = moles of Ca(HCO3)2
4. Convert the moles of CaCO3 to grams:
To do this, you need to determine the molar mass of CaCO3.
The molar mass of CaCO3 can be calculated as follows:
1 calcium (Ca) atom = 1 x 40.08 g/mol = 40.08 g/mol
1 carbon (C) atom = 1 x 12.01 g/mol = 12.01 g/mol
3 oxygen (O) atoms = 3 x 16.00 g/mol = 48.00 g/mol
Total molar mass = 40.08 + 12.01 + 48.00 = 100.09 g/mol
Now, multiply the moles of CaCO3 by the molar mass to get the mass in grams:
mass of CaCO3 = moles of CaCO3 x molar mass of CaCO3
5. Calculate the mass of limestone in kilograms:
Divide the mass of CaCO3 in grams by 1000 to convert it to kilograms:
mass of limestone = (mass of CaCO3 / 1000) kg
Now, let's calculate the mass of limestone:
moles of Ca(HCO3)2 = (4.93 x 10^13 g) / (162.12 g/mol) = 3.04 x 10^11 mol
moles of CaCO3 = moles of Ca(HCO3)2 = 3.04 x 10^11 mol
mass of CaCO3 = (3.04 x 10^11 mol) x (100.09 g/mol) = 3.05 x 10^13 g
mass of limestone = (mass of CaCO3 / 1000) kg = (3.05 x 10^13 g / 1000) kg = 3.05 x 10^10 kg
Therefore, the correct answer is 3.05 x 10^10 kg.