What would be the steps to solving this problem?
The aluminum sulfate hydrate [Al2(SO4)3 (times) xH2O] contains 8.20 % Al by mass. Calculate x, that is , the number of water molecules associated with each Al2(SO4)3 unit.
RMM for Al2(SO4)3
=27*2+(32+4*16)*3
=342
RMM for H2O
=2+16
=18
Number of water molecules = n
Thus
27*2/(342+18n)=0.082
Solve for n to get 18 (to 2 signinficant digits).
To calculate the number of water molecules associated with each Al2(SO4)3 unit in the aluminum sulfate hydrate, you can follow these steps:
Step 1: Convert the given mass percentage of aluminum (Al) to grams.
- If you have the mass of the hydrate, multiply it by the mass percentage (8.20%) to find the mass of aluminum.
Step 2: Calculate the moles of Al using its molar mass.
- Determine the molar mass of aluminum using the periodic table.
- Divide the mass of Al (in grams) by its molar mass to find the number of moles of Al.
Step 3: Determine the stoichiometric relationship between Al and H2O in the formula.
- The ratio of Al to H2O in the formula Al2(SO4)3 (times) xH2O is 2:3.
- This means that for every 2 moles of Al, there are 3 moles of H2O.
Step 4: Calculate the moles of H2O.
- Multiply the moles of Al (from step 2) by the ratio of H2O to Al (3/2) to find the moles of H2O.
Step 5: Convert the moles of H2O to grams.
- Determine the molar mass of water (H2O).
- Multiply the moles of H2O (from step 4) by its molar mass to find the mass of H2O.
Step 6: Calculate the number of water molecules (xH2O) using Avogadro's number.
- Divide the mass of H2O (in grams) by the molar mass of water.
- Multiply the result by Avogadro's number (6.022 x 10^23) to find the number of water molecules.
Step 7: Round the value of x to the nearest whole number.
- Since x represents the number of water molecules, it should be a whole number. Round the result from step 6 to the nearest whole number to determine x.
To solve this problem and determine the value of x, you need to follow these steps:
Step 1: Understand the given information.
The problem states that the aluminum sulfate hydrate [Al2(SO4)3 * xH2O] contains 8.20% Al by mass. This means that 8.20 g of Al is present in every 100 g of the compound.
Step 2: Find the molar mass of Al2(SO4)3.
Calculate the molar mass of Al2(SO4)3 by adding up the atomic masses of all the atoms present in the formula:
2(Al) + 3(S) + 12(O) = 2(26.98 g/mol) + 3(32.07 g/mol) + 12(16.00 g/mol)
Step 3: Calculate the mass of Al in 1 mol of Al2(SO4)3.
Using the periodic table, determine the molar mass of aluminum:
2(26.98 g/mol) = 53.96 g/mol
Step 4: Calculate the mass of water H2O in 1 mol of H2O.
Using the periodic table, determine the molar mass of water:
2(H) + 1(O) = 2(1.01 g/mol) + 16.00 g/mol
Step 5: Set up a proportion.
Now, set up a proportion using the given information and the calculated masses:
8.20 g Al / 100 g Al2(SO4)3 = y mol H2O / x mol Al2(SO4)3
Step 6: Solve for x.
Rearrange the proportion and solve for x:
x = (y mol H2O) * (100 g Al2(SO4)3) / (8.20 g Al)
Step 7: Convert moles to grams.
Multiply the molar mass of H2O by the calculated value of x to convert from moles to grams:
x g H2O = x mol H2O * (18.02 g/mol)
Step 8: Calculate the value of x.
Substitute the values into the equation, and solve for x:
x * 18.02 g/mol = (y mol H2O) * (100 g Al2(SO4)3) / (8.20 g Al)
By performing these calculations, you can determine the value of x, which represents the number of water molecules associated with each Al2(SO4)3 unit in the compound.
Thank You so much!
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