90.0g of magnesium chloride was placed in 50.0cm³water to give a saturated solution at 298k If the solubility of thesalt is 8.0mol/dm³ at the same temperature, what is the mass of the salt less dissolved at that given temperature [mg=24,Cl=35.5
To determine the mass of the salt less dissolved, we'll first calculate the number of moles of magnesium chloride dissolved in the saturated solution using its solubility. We'll then subtract this from the total moles of magnesium chloride initially present to find the amount of salt that remains undissolved.
First, let's calculate the number of moles of magnesium chloride dissolved in the solution. The solubility is given as 8.0 mol/dm³, which means that 1 dm³ (or 1000 cm³) of the solution contains 8.0 moles of magnesium chloride.
Given that the volume of water is 50.0 cm³, we need to convert it to dm³ before calculating the moles:
Volume of water = 50.0 cm³ = 50.0/1000 dm³ = 0.05 dm³
Now we can calculate the moles of magnesium chloride dissolved:
Moles of magnesium chloride dissolved = solubility × volume of water
= 8.0 mol/dm³ × 0.05 dm³
= 0.4 mol
Next, we need to find the molar mass of magnesium chloride (MgCl₂) to calculate the mass of the salt less dissolved. The molar mass of Mg is 24 g/mol, and the molar mass of Cl is 35.5 g/mol.
Molar mass of MgCl₂ = (molar mass of Mg) + 2 × (molar mass of Cl)
= (24 g/mol) + 2 × (35.5 g/mol)
= 95 g/mol
Now, we can calculate the mass of the salt less dissolved:
Mass of salt less dissolved = (total moles of magnesium chloride - moles of magnesium chloride dissolved) × molar mass of MgCl₂
= (90.0 g / 95 g/mol - 0.4 mol) × 95 g/mol
= (0.947 moles - 0.4 moles) × 95 g/mol
= 0.547 moles × 95 g/mol
= 51.965 g
Therefore, the mass of the salt less dissolved at the given temperature is approximately 52.0 g.