A0.8715 g sample of sorbic acid, a compound first obtained from the berries of a certain ash tree, is burned completely in oxygen to give 2.053 g of carbon dioxide and 0.5601 g of water. the empirical formula of sorbic acid is

C₃H₄O is the empirical formula of ascorbic acid

Explanation:

First, we need to write the reaction. I will call the Ascorbic Acid as AA:

AA + O₂ > CO₂ + H₂O

We know we have initially 0.8715 g of AA, and this produces 2.053 g of CO₂ and 0.5601 g of H₂O.

From the products, we can calculate how many moles of each element (C, H and O) has the ascorbic acid.

So, let's take in mind the molecular weight of CO₂ and H₂O:

MWCO₂ = 44 g/mol

MWH₂O = 18 g/mol

From the molecular weight we can calculate the moles of each product:

moles CO₂ = 2.053 / 44 = 0.0467 moles

moles H₂O = 0.5601 / 18 = 0.0311 moles

Now, with this, we can do a mole ratio of the elements. In the case of CO₂, we can calculate how many grams of Carbon are in the ascorbic acid, and with the water, the grams of hydrogen. Then, with difference we can get the mass of oxygen.

To do this ratio, we do a rule of 3.

To Carbon:

12 g C > 44 g CO₂

X g C > 2.053 g CO₂

X = 2.053 * 12/44 = 0.5599 g of C

For Hydrogen:

2 g H > 18 g H₂O

X g H > 0.5601 g H₂O

X = 2 * 0.5601/18 = 0.0622 g of H

We have the mass of C and H, so the grams of oxygen are:

m O = 0.8715 - 0.0622 - 0.5599 = 0.2494 g of O

Now that we have the mass of each element, we can calculate the empirical formula following 3 steps.

Step 1: Calculate the moles of each element

C = 0.5599 / 12 = 0.0467

H = 0.0622 / 1 = 0.0622

O = 0.2494 / 16 = 0.0156

Step 2: Calculate the mole ratio

Doing this, is just dividing all the moles by the smallest number of moles obtained. In this case, the oxygen so:

C = 0.0467/0.0156 = 2.99

H = 0.0622/0.0156 = 3.99

O = 0.0156/0.0156 = 1

These results represent the number of atoms of each element in the empirical formula, so the last step is write the empirical formula with the previous results, rounding the numbers to get an even number so:

C₃H₄O

This would be the empirical formula of ascorbic acid.

1. for the first question, we must find the mass of the anhydrous salt, mgso₄. the molar mass for mgso₄·7h₂o is 246.47 g/mol, while that of mgso₄ is 120.37 g/mol.7.834 g mgso₄·7h₂o * 1 mol mgso₄·7h₂o/246.47 g * 1 mol mgso₄/1 mol mgso₄·7h₂o * 20.37 g mgso₄/mol = 0.647 g mgso₄

2. mass of water = mass of sample - mass of anhydrous salemass of water = 7.834 - 0.647 = 7.19 gpercent water in hydrate = 7.19/7.834 * 100 = 91.74%