195 g of water containing magnesium chloride boils at 102.5 celcuis. what mass of salt is needed?
Let me check you work on this. The bp elevation is 2.5C
the answer is 30.1 grams magnesuim chloride but i don't kknow how to get to the answer
bpeleveation=m*constant
m=2.5/1.86
now m=moles/kgwater=moles/.195
moles=mass/formulamassMgCl2
mass=formulamass*.195*2.5/1.85
check all that math.
To find the mass of salt needed, we need to calculate the amount of magnesium chloride present in the given 195 g of water.
First, we need to determine the boiling point elevation constant (Kb) for water. For water, the Kb value is 0.512 °C/m. This means that for every 1 molal (1 mole of solute dissolved in 1 kg of water) concentration, the boiling point of water will increase by 0.512 °C.
Now, we can calculate the molality (m) of the magnesium chloride solution. Molality is defined as the number of moles of solute (magnesium chloride) dissolved in 1 kg of solvent (water).
Given:
Mass of water (solvent) = 195 g
Boiling point elevation = 102.5 °C
We can use the formula for boiling point elevation:
ΔTb = Kb * m
Rearranging the formula to solve for molality (m):
m = ΔTb / Kb
Substituting the values:
m = (102.5 °C - 100 °C) / 0.512 °C/m
m = 2.5 °C / 0.512 °C/m
m ≈ 4.88 molal
Now, we can calculate the mass of magnesium chloride using the molality and the molecular weight of magnesium chloride (95.211 g/mol).
Given:
Molecular weight of MgCl2 = 95.211 g/mol
Molality (m) = 4.88 molal
Mass of water (solvent) = 195 g
To find the moles of magnesium chloride (n):
n = m * mass of water (kg)
Converting the mass of water to kg:
mass of water (kg) = 195 g / 1000 = 0.195 kg
Now, calculating the moles of magnesium chloride:
n = 4.88 molal * 0.195 kg
n ≈ 0.95076 mol
Finally, we can find the mass of magnesium chloride using the moles and the molecular weight:
Mass of magnesium chloride = n * molecular weight
Mass of magnesium chloride = 0.95076 mol * 95.211 g/mol
Mass of magnesium chloride ≈ 90.58 g
Therefore, approximately 90.58 grams of magnesium chloride is needed for the given solution.