One of the main components of hard water is CaCO3. When hard water evaporates, some of the CaCO3 is left behind as a white mineral deposit. If hard water solution is saturated with calcium carbonate, what volume of the solution has to evaporate to deposite 1.00x10^2 mg of CaCO3
CaCO3 ==> Ca^2+ + CO3^2-
Look up Ksp.
Ksp = (Ca^2+)(CO3^2-)
Set up an ICE chart and solve for solubility CaCO3. That value will be in moles/L. Multiply by molar mass to obtain grams/L. Then convert to volume necessary to hold 100 mg. Post your work if you get stuck.
I took the square root of (4.96x10^-9)= 7.04x10^-5 mol/L
then 100.09g/mol x 7.04 mol/L= 7.05x 10^-3 g/L
then .100 g x 1 L/ 7.05x10^-3= 7.05x10^-4 L, so that was my final answer, does this seem right?
Trista is almost correct. However she failed to realize that the problem called for 100 mg which is equal to 0.1 grams. This means that (7.05x10^-3)g/L / 0.1g = 0.0705/1L (Where the L is in the denominator).
So in order to finalize this problem all you have to do is take the inverse to get 1L/0.0705 = 14.2 L
The correct anwser.
To calculate the volume of the hard water solution that needs to evaporate in order to deposit a given amount of CaCO3, we need to convert the given mass of CaCO3 to moles, and then use the stoichiometry of the reaction between CaCO3 and water to find the volume of the solution.
Here's how you can approach the problem:
1. Determine the molar mass of CaCO3:
- Ca: 40.08 g/mol
- C: 12.01 g/mol
- O: 16.00 g/mol (3 atoms)
Molar mass of CaCO3 = 40.08 + 12.01 + (16.00 x 3) = 100.09 g/mol
2. Convert the given mass of CaCO3 to moles:
Mass of CaCO3 = 1.00x10^2 mg = 0.1 g
Moles of CaCO3 = Mass of CaCO3 / Molar mass of CaCO3
= 0.1 g / 100.09 g/mol
3. Determine the stoichiometry of the reaction:
The reaction between CaCO3 and water is as follows:
CaCO3 + H2O → Ca2+ + HCO3- + OH-
From the chemical equation, we can see that 1 mol of CaCO3 produces 1 mol of Ca2+.
4. Calculate the volume of the solution using the stoichiometry:
Since 1 mole of CaCO3 is deposited, the volume of the solution can be found using the molar volume of water which is approximately 18 mL/mol.
Volume of the solution = Moles of CaCO3 x Molar volume of water
Note: Moles of CaCO3 = Moles of Ca2+ (according to stoichiometry)
Volume of the solution = (0.1 g / 100.09 g/mol) x 18 mL/mol
5. Calculate the final answer:
Calculate the volume of the solution from the previous step to get the answer in the desired units (e.g., mL or L).
Remember to pay attention to the units and conversions throughout the problem.