9.0g of hydrated salted CuSO4 x H2O was dissolved in 500cm3 of water and it's concentration in moldm3 was experimentally found to be 0.072M . Calculate, the molar mass of CuSO4 x H2O and the value of x, the water of crystallization.[Cu=64 S=32 O=16 H=1]
The number of cu2+ ions in 100cm3 of prepared solution.(L=6.02x10^23)
To calculate the molar mass of CuSO4 x H2O and the value of x, first we need to determine the number of moles of CuSO4 in the 500 cm3 of water.
Molarity (M) is defined as moles of solute per liter of solution. In this case, the concentration is given as 0.072 M, so:
0.072 M = moles of CuSO4 / 0.5 L
Rearranging the equation, we find:
moles of CuSO4 = 0.072 M * 0.5 L = 0.036 mol
The molar mass of CuSO4 is calculated by adding the atomic masses of copper (Cu), sulfur (S), and four oxygen atoms (O):
Molar mass of CuSO4 = (1 Cu * 64 g/mol) + (1 S * 32 g/mol) + (4 O * 16 g/mol) = 159 g/mol
Now, we can find the molar mass of CuSO4 x H2O by adding the molar mass of CuSO4 to the molar mass of water (H2O):
Molar mass of CuSO4 x H2O = 159 g/mol + molar mass of water
Let's assume the molar mass of water is m g/mol. Since we have 9.0 g of hydrated CuSO4 x H2O, we can write:
9.0 g = 0.036 mol * (159 g/mol + m g/mol)
Solving for m:
m = (9.0 g - 0.036 mol * 159 g/mol) / 0.036 mol
m ≈ 144 g/mol
So, the molar mass of CuSO4 x H2O is approximately 159 g/mol + 144 g/mol = 303 g/mol.
Finally, to determine the value of x, the water of crystallization, we divide the molar mass of water by the molar mass of CuSO4 x H2O:
x = (molar mass of water) / (molar mass of CuSO4 x H2O)
x = 144 g/mol / 303 g/mol ≈ 0.475
Therefore, the value of x, the water of crystallization, is approximately 0.475.
To find the number of Cu2+ ions in 100 cm3 of the prepared solution, we need to know the concentration of Cu2+ ions in the solution. Since CuSO4 is a 1:1 salt, the concentration of Cu2+ ions is equal to the concentration of CuSO4 in the solution, which is given as 0.072 M.
The number of moles of Cu2+ ions in 100 cm3 of solution is calculated as:
moles of Cu2+ ions = concentration of Cu2+ ions * volume of solution
moles of Cu2+ ions = 0.072 M * 0.1 L = 0.0072 mol
Since 1 mole contains 6.02x10^23 particles, the number of Cu2+ ions in 100 cm3 of the prepared solution is:
number of Cu2+ ions = moles of Cu2+ ions * Avogadro's number
number of Cu2+ ions = 0.0072 mol * 6.02x10^23 mol^-1 = 4.33x10^21 ions.
Therefore, the number of Cu2+ ions in 100 cm3 of the prepared solution is approximately 4.33x10^21 ions.
To calculate the molar mass of CuSO4 x H2O and the value of x, we first need to determine the moles of CuSO4 in the solution and then relate it to the molar mass.
Step 1: Calculate the moles of CuSO4
Moles = Concentration x Volume
Moles = 0.072M x 0.500L (since 500cm3 is equal to 0.500L)
Moles = 0.036 mol
Step 2: Determine the molar mass of CuSO4
Molar mass of Cu = 64 g/mol
Molar mass of S = 32 g/mol
Molar mass of O (4 atoms) = 16 g/mol x 4 = 64 g/mol
Total molar mass of CuSO4 = 64 g/mol + 32 g/mol + 64 g/mol = 160 g/mol
Step 3: Determine the molar mass of CuSO4 x H2O
Since the molar mass of CuSO4 is 160 g/mol, and there is also water of crystallization (H2O) present, we need to consider its mass.
Let's assume the molar mass of H2O is M.
Molar mass of CuSO4 x H2O = 160 g/mol + 18 g/mol (2H + O) = 178 g/mol
Step 4: Calculate the value of x (water of crystallization)
The molar mass of CuSO4 x H2O is 178 g/mol.
Since the moles of CuSO4 in the solution is 0.036 mol, we can set up the equation:
178 g/mol = (0.036 mol + x mol) g/mol
Solving the equation:
178 = (0.036 + x) * 178
178 = 6.408 + 178x
178x = 171.592
x = 171.592 / 178
x ≈ 0.964
So, the value of x is approximately 0.964, indicating the presence of approximately 0.964 moles of water of crystallization (H2O) in CuSO4 x H2O.
Step 5: Calculate the number of Cu2+ ions in 100 cm3 of the prepared solution.
The moles of CuSO4 in 100 cm3 of the solution can be calculated using the concentration and volume.
Moles = Concentration x Volume
Moles = 0.072M x 0.100L (since 100cm3 is equal to 0.100L)
Moles = 0.0072 mol
Each mole of CuSO4 contains one mole of Cu2+ ions.
Therefore, there are 0.0072 moles of Cu2+ ions in 100 cm3 of the solution.
To calculate the number of Cu2+ ions, we can use Avogadro's number (L = 6.02x10^23) to convert from moles to particles.
Number of Cu2+ ions = Moles x Avogadro's number
Number of Cu2+ ions = 0.0072 mol x 6.02x10^23 particles/mol
Solving for the number of Cu2+ ions:
Number of Cu2+ ions ≈ 4.344x10^21 ions
Thus, there are approximately 4.344x10^21 Cu2+ ions in 100 cm3 of the prepared solution.