sodium metal dissolves in liquid mercury to form a solution called a sodium amalgam. the densities of Na(s) and Hg(l) are 0.97g/mL and 13.6g/mL. a sodium amalgam is made by dissolving 1.0 mL Na(s) in 20.0 mL Hg(l). the final volume is 21.0 mL. What is the molality of Na in the solution
To find the molality of sodium (Na) in the solution, we need to calculate the moles of sodium and the mass of the solvent (mercury).
First, let's calculate the moles of sodium:
Given:
Density of sodium (Na) (ρNa) = 0.97 g/mL
Volume of sodium (VNa) = 1.0 mL
To find the mass (m) of sodium, we can use the formula:
m = ρ × V
Where ρ is the density and V is the volume.
mNa = ρNa × VNa
mNa = 0.97 g/mL × 1.0 mL
mNa = 0.97 g
Next, let's calculate the moles of mercury (Hg):
Given:
Density of mercury (Hg) (ρHg) = 13.6 g/mL
Volume of mercury (VHg) = 20.0 mL
mHg = ρHg × VHg
mHg = 13.6 g/mL × 20.0 mL
mHg = 272 g
Now, we can calculate the molality (m) of sodium:
Molality (m) = (moles of solute) / (mass of solvent in kg)
To find the moles of sodium (Na), we can use the formula:
moles = mass / molar mass
Molar mass of sodium (Na) (MMNa) = 22.99 g/mol
moles of Na = mNa / MMNa
moles of Na = 0.97 g / 22.99 g/mol
moles of Na = 0.04215 mol
Since the final volume of the solution is 21.0 mL, we need to convert it to kg:
Volume of solution (Vs) = 21.0 mL
Density of solution (ρs) = total mass / total volume
To find the total mass, we can sum the mass of sodium and mercury:
Total mass = mNa + mHg
Total mass = 0.97 g + 272 g
Total mass = 272.97 g
ρs = Total mass / Vs
ρs = 272.97 g / 21.0 mL
To convert mL to L:
ρs = 272.97 g / 0.021 L
ρs = 13,045.57 g/L
Now let's calculate the molality:
Molality (m) = (moles of solute) / (mass of solvent in kg)
Mass of solvent (ms) = (ρs - ρNa × VNa) / 1000
ms = (13,045.57 g/L - 0.97 g/mL × 1.0 mL) / 1000
ms = (13,045.57 g/L - 0.97 g) / 1000
ms = 13,044.6 g/L / 1000
ms = 13.0456 g
Molality (m) = moles of Na / mass of solvent in kg
m = 0.04215 mol / 13.0456 kg
m = 0.003229 mol/kg
Therefore, the molality of sodium (Na) in the solution is approximately 0.00323 mol/kg.