In a mountainous location, the boiling point of pure water is found to be 95 degrees Celsius. How many grams of sodium chloride much be added to 1 kg of water to bring the boiling point back to 100 degrees Celsius? Assume that sodium chloride behaves ideally in solution.
Dr. Bob do you use 1kg of water in the m=moles/kg so it would be 4.8528=1mol/1kg
280.43g of NaCl is needed to raise the boiling point to 100 degrees.
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To solve this problem, we need to use the concept of boiling point elevation, which states that adding a non-volatile solute to a solvent will increase the boiling point of the solvent.
We can use the formula for boiling point elevation:
ΔTb = Kb * m
Where:
- ΔTb is the change in boiling point
- Kb is the molal boiling point elevation constant (which is unique to each solvent)
- m is the molality of the solute (moles of solute per kg of solvent)
In this case, we want to calculate how much sodium chloride (NaCl) needs to be added to 1 kg of water to bring the boiling point back to 100 degrees Celsius. We know that in the mountainous location, the boiling point of pure water is 95 degrees Celsius.
First, let's calculate the change in boiling point (ΔTb):
ΔTb = 100°C - 95°C = 5°C
Next, we need to find the molal boiling point elevation constant for water (Kb). For water, Kb is approximately 0.512 °C/m.
Now, we can rearrange the formula to solve for molality (m):
m = ΔTb / Kb
m = 5°C / 0.512 °C/m
m ≈ 9.77 mol/kg
This means that for every 1 kg of water, we need to add approximately 9.77 moles of sodium chloride.
Finally, we need to convert moles to grams by using the molar mass of sodium chloride, which is approximately 58.44 g/mol:
Mass of NaCl = m * molar mass of NaCl
Mass of NaCl ≈ 9.77 mol * 58.44 g/mol
Mass of NaCl ≈ 570.8 g
Therefore, approximately 571 grams of sodium chloride (NaCl) should be added to 1 kg of water to bring the boiling point back to 100 degrees Celsius.
delta T = i*Kb*m
delta T = 5; Kb = 0.512; i = 2. Solve for m
m = moles/kg
solve for moles.
moles = grams/molar mass
solve for grams.