If you have 0.50M Ca(NO3)2 solution, how many mL of this solution must be evaporated to obtain 32.8 grams of solid Ca(NO3)2?
To find out how many milliliters (mL) of the Ca(NO3)2 solution must be evaporated, we can use the concept of the molarity of a solution.
Molarity (M) is defined as the number of moles of solute (Ca(NO3)2 in this case) per liter (L) of solution.
First, we need to calculate the number of moles of Ca(NO3)2 in the solid required:
Given that the mass of Ca(NO3)2 is 32.8 grams, we need to convert this mass into moles. The molar mass of Ca(NO3)2 can be calculated by adding up the atomic masses of its elements:
Ca: 40.08 g/mol
N: 14.01 g/mol
O: 16.00 g/mol (x2 for two oxygen atoms)
Adding these together, we get:
Ca(NO3)2 molar mass = (40.08 g/mol) + (14.01 g/mol) + (16.00 g/mol x 2) = 164.09 g/mol
Now, we can find the number of moles of Ca(NO3)2 required by dividing the given mass by the molar mass:
Number of moles = mass / molar mass
Number of moles = 32.8 g / 164.09 g/mol ≈ 0.1998 mol
Next, we can determine the volume of the Ca(NO3)2 solution required to contain this number of moles.
Since the given solution has a molarity of 0.50 M, this means that 1 liter (1000 mL) of the solution contains 0.50 moles of Ca(NO3)2.
We can set up a proportion to find the volume (V) of the solution required to contain the desired number of moles:
0.50 moles / 1000 mL = 0.1998 moles / V mL
Now, we can solve for V:
V mL = 0.1998 moles / (0.50 moles / 1000 mL)
V mL = 0.1998 moles * (1000 mL / 0.50 moles)
V mL ≈ 399.6 mL
Therefore, approximately 399.6 mL of the Ca(NO3)2 solution must be evaporated to obtain 32.8 grams of solid Ca(NO3)2.