An unknown salt AS x XH2O was analyzed and found to contain 16.4 percent water. If the anhydrous salt has a formula mass of 183 amu, find the water of crystallization (X) for the hydrate.
I have no idea how to figure this out! HELPP PLEASE!!
To determine the water of crystallization (X) for the hydrate, we can use the concept of percent composition.
Step 1: Find the molar mass of the anhydrous salt (AS).
Given that the formula mass of the anhydrous salt is 183 amu, we can assume that the formula mass represents one mole of the anhydrous salt.
Therefore, the molar mass of the anhydrous salt (AS) is 183 g/mol.
Step 2: Determine the molar mass of the water (H2O).
The molar mass of water (H2O) can be calculated by adding the atomic masses of hydrogen (H) and oxygen (O).
The atomic mass of hydrogen is 1 g/mol, and the atomic mass of oxygen is 16 g/mol. Therefore, the molar mass of water is 18 g/mol.
Step 3: Calculate the percent composition of water in the hydrate.
Given that the salt contains 16.4 percent water, we can assume that the remaining percentage (100% - 16.4%) represents the anhydrous salt.
The percent composition of the anhydrous salt:
100% - 16.4% = 83.6%
Step 4: Calculate the molar amount of each component in the hydrate.
To find the molar amount of each component, we need to convert the percentages to grams.
For the water component:
16.4% of A grams = 16.4/100 * A
A = (16.4 * 100) /16.4
A = 100 grams
For the anhydrous salt component:
83.6% of B grams = 83.6/100 * B
B = (83.6 * 100) / 83.6
B = 100 grams
Step 5: Convert the grams to moles for each component.
To convert grams to moles, divide the given mass by the molar mass.
Moles of water (H2O) = 100 g / 18 g/mol ≈ 5.56 mol
Moles of anhydrous salt (AS) = 100 g / 183 g/mol ≈ 0.55 mol
Step 6: Determine the ratio between the moles of water (X) and the moles of anhydrous salt (AS).
Divide the number of moles of water (5.56 mol) by the number of moles of anhydrous salt (0.55 mol) to find the ratio.
Ratio = 5.56 mol / 0.55 mol ≈ 10
Therefore, the water of crystallization (X) for the hydrate is 10, meaning that the hydrate contains 10 moles of water molecules per mole of anhydrous salt.
To solve this problem, we can use the concept of percent composition and the formula mass of the hydrate.
Let's assume that x is the number of water molecules (XH2O) in the hydrate.
Step 1: Determine the formula mass of the hydrate
The formula mass of the hydrate is the sum of the masses of all the atoms in the formula. In this case, it consists of the anhydrous salt (AS) and x water molecules (x XH2O). We are given that the formula mass of the anhydrous salt (AS) is 183 amu.
Step 2: Determine the mass of water in the hydrate
Since the hydrate contains 16.4% water, this means that in 100 grams of the hydrate, 16.4 grams are water. Therefore, we can calculate the mass of water in x water molecules (x XH2O) as (16.4 grams / 100 grams) * x.
Step 3: Determine the mass of the anhydrous salt in the hydrate
The remaining mass in 100 grams of the hydrate after subtracting the mass of water (16.4 grams) is the mass of the anhydrous salt. Therefore, we can calculate the mass of the anhydrous salt as 100 grams - 16.4 grams.
Step 4: Set up an equation based on mole-to-mole ratio
Since the formula mass of the anhydrous salt (AS) is given as 183 amu, and we know the mass of the anhydrous salt in grams from the previous step, we can convert the mass to moles using the molar mass.
Step 5: Determine the mole-to-mole ratio between water and the anhydrous salt
The mole-to-mole ratio between water and the anhydrous salt can be found by comparing the coefficients of the formula. In this case, since the water of crystallization is expressed as x, the mole-to-mole ratio between water and the anhydrous salt is 1:x.
Step 6: Solve for x
Now that we have all the necessary information, we can set up an equation to solve for x by equating the moles of water to the moles of the anhydrous salt.
Mass of water / molar mass of water = Moles of water
Moles of water (from previous calculation) * (1 mole anhydrous salt/x moles water) = Moles of anhydrous salt
Now we can solve for x:
Moles of anhydrous salt = Moles of water * (x/1)
Step 7: Calculate x
Substitute the values we calculated into the equation and solve for x:
(Mass of water / molar mass of water) * (x/1) = Mass of anhydrous salt / molar mass of anhydrous salt
(16.4 grams / 18.02 g/mol) * (x/1) = (100 grams - 16.4 grams) / 183 g/mol
Simplifying the equation:
(0.9101) * (x/1) = (83.6 grams) / 183 g/mol
0.9101x = 0.4568
x = 0.50
Therefore, the water of crystallization (X) for the hydrate is 0.50 or 1/2. So the formula of the hydrate is AS · 1/2 H2O.