In the course of research, a chemist isolates a new compound with an empirical formula C3H3O2. 4.97 g of the compound when dissolved in 100. g of water produces a solution with a freezing point of −0.325°C. What is the molecular formula of the compound? (For water, Kf = 1.86°C/m.) (For your answer, enter the integer that tells the number of multiples of the empirical formula present in the molecular formula.)
You can find the molal concentration (m) from 0.325degC/(1.86degC/m)
m=(number of moles)/0.1 kg
hence find number of moles.
molecular mass = (mass used)/(number of moles)= 4.97g/(number of moles).
RMM of C3H3O2 = 71
multiple = molecular mass/71
As a point of interest a compound that only contains C, H and O must have an even numebr of hydrogen atoms. Hence the multiple must be an even number.
To determine the molecular formula of the compound, we need to find the molar mass of the compound first. Here's how you can do it:
1. Start by finding the molar mass of the empirical formula (C3H3O2):
- The molar mass of carbon (C) is 12.01 g/mol.
- The molar mass of hydrogen (H) is 1.01 g/mol.
- The molar mass of oxygen (O) is 16.00 g/mol.
- Calculate the molar mass of the empirical formula:
(3 * 12.01 g/mol) + (3 * 1.01 g/mol) + (2 * 16.00 g/mol) = 57.08 g/mol.
2. Now, we need to find the freezing point depression (∆Tf) of the solution caused by dissolving the compound in water:
- The freezing point depression is the difference between the freezing point of the pure solvent (water) and the freezing point of the solution.
- ∆Tf = Pure solvent freezing point - Solution freezing point.
- The freezing point of pure water is 0°C.
- The solution freezing point is -0.325°C.
- Therefore, ∆Tf = 0°C - (-0.325°C) = 0.325°C.
3. Lastly, we can use the freezing point depression to calculate the molality (m) of the solution:
- Molality (m) is defined as the number of moles of the solute (compound) per kilogram of the solvent (water).
- ∆Tf = Kf * m,
where Kf is the cryoscopic constant (1.86°C/m),
and m is the molality of the solution.
- Rearranging the equation to solve for m:
m = ∆Tf / Kf = 0.325°C / 1.86°C/m = 0.1747 m.
4. Convert the mass of the compound (4.97 g) to moles:
- Moles of compound = mass of compound / molar mass of the compound.
- Moles of compound = 4.97 g / 57.08 g/mol ≈ 0.087 moles.
5. Finally, using the empirical formula, find the number of multiples of the empirical formula present in the molecular formula:
- Divide the moles of the compound by 0.087 moles (the empirical formula molar ratio):
Number of multiples = moles of compound / 0.087 moles.
Now you can use the given information to calculate the number of multiples of the empirical formula in the molecular formula.