calculate the molarity of a copper ii nitrate solution with a density of 1.48 g/ml and a percent mass by mass of 5.20 %
5.20% w/w means 5.20 g Cu(NO3)2 in 100 g solution.
1. Convert 5.20g to mols. mols = grams/molar mass.
2. Convert 100 g solution to mL using density. mass = volume x density or volume = mass/density = 100g/1.48 and convert mL to L.
3. Then M = mols from step 1/L from step 2
To calculate the molarity of a copper II nitrate solution, you need to know the molar mass of copper II nitrate. The molar mass is the sum of the atomic masses of all the atoms in a molecule.
First, let's calculate the molar mass of copper II nitrate (Cu(NO3)2):
- Copper (Cu) has an atomic mass of 63.55 g/mol.
- Nitrogen (N) has an atomic mass of 14.01 g/mol.
- Oxygen (O) has an atomic mass of 16.00 g/mol.
Molar mass of copper II nitrate (Cu(NO3)2):
= (63.55 g/mol) + 2 * [(14.01 g/mol) + 3 * (16.00 g/mol)]
= 63.55 g/mol + 2 * (14.01 g/mol + 48.00 g/mol)
= 63.55 g/mol + 2 * 62.01 g/mol
= 63.55 g/mol + 124.02 g/mol
= 187.57 g/mol
Now that we have the molar mass of copper II nitrate, we can proceed to calculate the molarity using the given information.
Step 1: Calculate the mass of copper II nitrate in the solution:
To determine the mass of copper II nitrate, we will use the density and volume of the solution.
Given:
Density of the solution = 1.48 g/ml
Percent mass by mass = 5.20 %
To calculate the mass, divide the percent mass by 100 and multiply by the total mass of the solution.
Mass of solution = density * volume
Let's assume we have 100 mL of the solution for easier calculations.
Mass of solution = (1.48 g/ml) * (100 ml) = 148 g
Mass of copper II nitrate in the solution = (5.20 / 100) * (148 g) = 7.696 g
Step 2: Calculate the moles of copper II nitrate:
To calculate the moles, divide the mass of copper II nitrate by its molar mass.
Moles of copper II nitrate = mass / molar mass
= 7.696 g / 187.57 g/mol = 0.04102 mol
Step 3: Calculate the volume of the solution in liters:
Since molarity is defined as moles of solute per liter of solution, we need to convert the volume from milliliters (ml) to liters (L).
Volume of solution in liters = 100 mL / 1000 mL/L = 0.1 L
Step 4: Calculate the molarity of the copper II nitrate solution:
Molarity is the number of moles of solute divided by the volume of the solution in liters.
Molarity (M) = Moles of solute / Volume of solution (L)
= 0.04102 mol / 0.1 L = 0.4102 M
Therefore, the molarity of the copper II nitrate solution with a density of 1.48 g/ml and a percent mass by mass of 5.20% is 0.4102 M.