Analysis of a compound indicates that it is 49.02% carbon, 2.743% hydrogen, and 48.23% chlorine by mass. A solution is prepared by dissolving 3.150 grams of the compound in 25.00 grams of benzene, C6H6. Benzene has a normal freezing point of 5.50degreeC and the solution freezes at 1.12degreeC. The molal freezing point constant,kf, for benzene is 5.12C/molal.
1.Find the empirical formula of this compound.
2.Using the freezing point data calculate the molar mass of the compound.
3. Calculate the mole fraction of benzene in the solution.
4. The vapor pressure of benzene at 35degreeC is 150.0mmHg. Calculate the vapor pressure of benzene over the solution described in this problem at 35degreeC.
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To solve these problems, we need to follow a step-by-step approach. Let's tackle each question one by one.
1. Finding the empirical formula of the compound:
To determine the empirical formula, we need to find the ratio of the elements present in the compound. We are given the percentages of carbon, hydrogen, and chlorine by mass.
The first step is to convert these percentages into grams. Let's assume we have 100 grams of the compound.
- Carbon: 49.02 grams (49.02% of 100g)
- Hydrogen: 2.743 grams (2.743% of 100g)
- Chlorine: 48.23 grams (48.23% of 100g)
Next, we need to convert these masses into moles. To do this, we divide each mass by the atomic mass of the corresponding element:
- Carbon: 49.02 / atomic mass of carbon (12.01 g/mol)
- Hydrogen: 2.743 / atomic mass of hydrogen (1.01 g/mol)
- Chlorine: 48.23 / atomic mass of chlorine (35.45 g/mol)
Now, calculate the mole ratio of the elements by dividing each number of moles by the smallest number of moles obtained. Round the ratios to the nearest whole number:
- Carbon: determine the closest whole number ratio by dividing the number of moles of carbon by the smallest number of moles obtained.
- Hydrogen: determine the closest whole number ratio by dividing the number of moles of hydrogen by the smallest number of moles obtained.
- Chlorine: determine the closest whole number ratio by dividing the number of moles of chlorine by the smallest number of moles obtained.
The obtained whole numbers represent the subscripts in the empirical formula of the compound.
2. Calculating the molar mass of the compound:
To calculate the molar mass of the compound, we need the empirical formula determined in the previous step. Multiply the atomic masses of each element in the empirical formula by the respective subscripts and sum them up.
3. Calculating the mole fraction of benzene in the solution:
The mole fraction of benzene (C6H6) can be calculated using the following formula:
Mole fraction of benzene = moles of benzene / (moles of benzene + moles of compound)
To find the moles of benzene, divide the mass of benzene by the molar mass of benzene. The moles of the compound can be obtained from the previous calculations.
4. Calculating the vapor pressure of benzene over the solution:
To calculate the vapor pressure of benzene over the solution, we need to use Raoult's law, which states that the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent multiplied by its vapor pressure in pure form.
The vapor pressure of benzene in pure form is given (150.0 mmHg at 35°C). Multiply this vapor pressure by the mole fraction of benzene (calculated in the previous step) to obtain the vapor pressure of benzene over the solution at 35°C.