Answer:
Molarity = 0.9 M
Molality = 0.95 m
Step-by-step explanation:
Data given:
mass of CaCl₂ = 23 g
mass of water = 217g
Density of water = 1g/mol
molality of solution = ?
molarity of solution = ?
Solution:
Molarity and Molality are terms used for concenteration of solution
Formula Used for Molarity
Molarity = moles of solute / liter of solution . . . . . (1)
So first we find number of moles of 23 g CaCl₂.
Formula used to find moles
no. of moles = mass in g / molar mass
molar mass CaCl₂ = 40 + 2(35.5)
molar mass CaCl₂ = 40 + 71 = 111 g/ mole
So,
Put values in mole formula
no. of moles = 23 g / 111 g/mol
no. of moles = 0.21 mol
Now,
As for molarity we have to convert grams of water to liter
for this purpose we will use density formula
d= m/v
for volume rearrange the above equation
v = m/d . . . . . . . (2)
put vlue in above equation 2
v = 217 g / 1 (g/mL)
v = 217 mL
Now,
Total amount of solution = 23 + 217 = 240 mL
Now, Convert the mL to Liter
1000 = 1 L
240 mL = 240 /1000 = 0.24 L
So no we have the following required values to find molarity
no. of moles of CaCl₂ = 0.21 mol
liter of solution = 0.24 L
Put values in equation 1
Molarity = 0.21 mol / 0.24 L
Molarity = 0.9 M
_______________
To find Molality (m)
Formula used to find Molality
Molality = moles of solute / kg of solvent . . . . . . . (3)
So, no we have to convert grams of water to Kg
1000 g = 1 kg
217 g = 217 / 1000 = 0.22 Kg
Now,
Put values in equation
Molality = 0.21 mol / 0.22 kg
Molality = 0.95 m
So, the Molality = 0.95 m