What is the mass of NaCl required to make 840. mL of solution having an osmotic pressure of 7.70 atm at 36.6°C? This is the approximate concentration of the saline solution used to rinse contact lenses.
pi = osmotic pressure in atm = i*M*RT
You know pi in atm.
i = van't Hoff factor which is 2 for NaCl
R = 0.08205 = universal gas constant
T = kelvin temperature
Solve for M = molarity
Then M = mols/L.You have L, solve for mols and mols = g/molar mass NaCl.solve for g NaCl. Post your work if you get stuck.
To find the mass of NaCl required to make the given solution, we need to use the formula for osmotic pressure and the ideal gas law. Here's how you can calculate it:
1. Start by converting the given volume from milliliters (mL) to liters (L):
840 mL = 0.840 L
2. Next, we need to convert the temperature from Celsius (°C) to Kelvin (K):
T(°C) + 273.15 = T(K)
36.6°C + 273.15 = 309.75 K
3. Now, we can use the formula for osmotic pressure:
π = i * n * R * T / V
π = osmotic pressure
i = van't Hoff factor (number of particles NaCl dissociates into; for NaCl, it is 2)
n = moles of solute (NaCl)
R = ideal gas constant (0.0821 L*atm/(mol*K))
T = temperature in Kelvin
V = volume of solution in liters
Rearranging the formula, we get:
n = (π * V) / (i * R * T)
Substituting the given values into the formula, we have:
n = (7.70 atm * 0.840 L) / (2 * 0.0821 L*atm/(mol*K) * 309.75 K)
4. Calculate the moles of NaCl:
n = 0.2172 mol
5. Finally, we need to convert moles to mass. The molar mass of NaCl is 58.44 g/mol.
m = n * M
m = 0.2172 mol * 58.44 g/mol
The mass of NaCl required to make the solution is approximately 12.68 grams.