An aqueous sodium salt (NaCnH2n+1O3) solution has an osmotic pressure of 2.041 atm when 1.068 g of the salt are dissolved in 200. g of water at 25 degrees C. Assuming molality and molarity in such a dilute solution are the same and that the sodium salt is completely dissociated in the solution, determine the formula for the sodium salt.
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To determine the formula for the sodium salt (NaCnH2n+1O3), we need to consider the osmotic pressure and the amount of salt dissolved in the solution.
First, let's convert the given mass of the salt to moles.
The molecular weight of the salt can be calculated by adding the atomic masses of the constituent elements:
Molar mass of NaCnH2n+1O3 = (23 + 12n + 1.01(2n + 1) + 16(3)) g/mol = (47n + 49) g/mol
Now we can calculate the number of moles of the salt:
moles of salt = mass of salt / molar mass of salt
= 1.068 g / (47n + 49) g/mol
Next, we need to calculate the molality of the solution. Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water.
molality (m) = moles of solute / mass of water (in kg)
= moles of salt / mass of water (in kg)
Given that the mass of water is 200 g, we need to convert it to kg:
mass of water = 200 g = 0.2 kg
Now we can rearrange the formula for molality:
moles of salt = molality x mass of water
Substituting the values, we get:
1.068 g / (47n + 49) g/mol = molality x 0.2 kg
Simplifying the equation, we get:
molality = (1.068 / (47n + 49)) / 0.2
Finally, we can use the provided osmotic pressure and the formula for osmotic pressure to determine the value of n in the sodium salt.
The formula for osmotic pressure, in an ideal solution of a nonvolatile solute, is given by:
osmotic pressure = (nRT) / V
Where:
n = number of moles of solute
R = ideal gas constant (0.0821 L atm / mol K)
T = temperature in Kelvin (25 + 273 = 298 K)
V = volume of solution in liters
In this case, the volume of the solution is not given, but since the solution is dilute, we can assume that the volume of water is approximately equal to the volume of the solution.
Substituting the given values, we have:
2.041 atm = (n x 0.0821 L atm / mol K x 298 K) / V
We can solve this equation for the value of n. Once we find the value of n, we can determine the empirical formula of the sodium salt by counting the number of atoms of each element in the formula and simplifying if needed.
By following these steps, we can determine the formula for the sodium salt (NaCnH2n+1O3).