Let's solve this problem step-by-step:
### Step 1: Calculate the Mass of the Hydrated Salt
To find the mass of the hydrated salt, we subtract the mass of the crucible from the combined mass of the crucible and the hydrated salt:
[tex]\[
\text{Mass of hydrated salt} = 21.447\, \text{g} - 17.985\, \text{g} = 3.462\, \text{g}
\][/tex]
So, the mass of the hydrated salt is [tex]\(3.462\, \text{g}\)[/tex].
### Step 2: Calculate the Mass of the Anhydrous Salt
Next, we calculate the mass of the anhydrous salt by subtracting the mass of the crucible from the combined mass of the crucible and the anhydrous salt:
[tex]\[
\text{Mass of anhydrous salt} = 20.070\, \text{g} - 17.985\, \text{g} = 2.085\, \text{g}
\][/tex]
So, the mass of the anhydrous salt is [tex]\(2.085\, \text{g}\)[/tex].
### Step 3: Calculate the Mass of Water Lost During Heating
The mass of water lost during heating is determined by subtracting the mass of the anhydrous salt from the mass of the hydrated salt:
[tex]\[
\text{Mass of water lost} = 3.462\, \text{g} - 2.085\, \text{g} = 1.377\, \text{g}
\][/tex]
So, the mass of water lost is [tex]\(1.377\, \text{g}\)[/tex].
### Step 4: Calculate the Percent Water in the Hydrate
Finally, to find the percent of water in the hydrate, we divide the mass of the water lost by the mass of the hydrated salt and then multiply by 100:
[tex]\[
\text{Percent water} = \left( \frac{1.377\, \text{g}}{3.462\, \text{g}} \right) \times 100 = 39.7747\%
\][/tex]
So, the percent of water in the hydrate is approximately [tex]\(39.77\%\)[/tex].
