Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as MgSO4 · x H2O, where x indicates the number of moles of H2O per mole of MgSO4. When 5.469 g of this hydrate is heated to 250°C, all the water of hydration is lost, leaving 2.671 g of MgSO4. What is the value of x?
To find the value of x, we need to use the given information and perform a step-by-step calculation.
1. Calculate the mass of water lost:
Mass of water lost = Initial mass of hydrate - Mass of anhydrous compound
Mass of water lost = 5.469 g - 2.671 g
Mass of water lost = 2.798 g
2. Determine the molar mass of water (H2O):
Molar mass of H = 1 g/mol
Molar mass of O = 16 g/mol
Molar mass of H2O = 2 * (1 g/mol) + (16 g/mol) = 18 g/mol
3. Calculate the number of moles of water lost:
Moles of water lost = Mass of water lost / Molar mass of H2O
Moles of water lost = 2.798 g / 18 g/mol
Moles of water lost = 0.1554 mol
4. Determine the number of moles of MgSO4:
Moles of MgSO4 = Mass of anhydrous compound / Molar mass of MgSO4
Moles of MgSO4 = 2.671 g / (24.31 g/mol + 32.06 g/mol + (4 * 16 g/mol))
Moles of MgSO4 = 2.671 g / 120.367 g/mol
Moles of MgSO4 = 0.0222 mol
5. Find the mole ratio of water to MgSO4:
Moles of water lost / Moles of MgSO4 = x / 1
0.1554 mol / 0.0222 mol = x / 1
6. Solve for x:
x = (0.1554 mol / 0.0222 mol) * 1
x = 6.992
Therefore, the value of x in the formula MgSO4 · x H2O is 6.992.
To find the value of x in MgSO4 · x H2O, we need to determine the number of moles of water lost when 5.469 g of the hydrate is heated.
The molar mass of MgSO4 can be calculated as follows:
Mg = 24.305 g/mol
S = 32.06 g/mol
O4 = (16.00 g/mol) * 4 = 64.00 g/mol
Adding these values together, we get:
MgSO4 = 24.305 g/mol + 32.06 g/mol + 64.00 g/mol = 120.365 g/mol
Next, we will calculate the number of moles of MgSO4:
moles of MgSO4 = mass / molar mass
moles of MgSO4 = 2.671 g / 120.365 g/mol = 0.0222 mol
From the balanced chemical equation, we know that for every 1 mole of MgSO4, x moles of H2O are present. Therefore, we can set up a proportion:
moles of H2O / moles of MgSO4 = x / 1
Plugging in the values we have:
moles of H2O / 0.0222 mol = x / 1
Now, we need to determine the number of moles of H2O. We can do this by subtracting the mass of MgSO4 from the original mass of the hydrate:
mass of H2O lost = mass of hydrate - mass of MgSO4
mass of H2O lost = 5.469 g - 2.671 g = 2.798 g
To calculate the moles of H2O:
moles of H2O = mass / molar mass
moles of H2O = 2.798 g / 18.015 g/mol = 0.1554 mol
Plugging this value back into the proportion, we have:
0.1554 mol / 0.0222 mol = x / 1
Simplifying the equation:
7 = x / 1
Therefore, x = 7.
So, the value of x in MgSO4 · x H2O is 7.
5.469 g = mass MgSO4 + xH2O
-2.671 g = mass MgSO4
--------------
2.798 g = mass H2O
mols MgSO4 = 2.671/molar mass = ?
mols H2O = 2.798/molar mass H2O = ?
Now find the ratio for 1 mol MgSO4. The easy way to do that is to divide mols MgSO4 by itself (which automatically gives you 1.00), then divide the mols H2O by the same value to find x.
Post your work if you run into trouble.