Final answer:
To find the mass percent of water in the hydrated salt, the total mass of 8 moles of water is calculated then added to the molar mass of the anhydrous salt. This sum is used to find the mass percent by dividing the mass of water by the total mass of the hydrated salt and multiplying by 100, yielding a mass percent of 47.358% after rounding to three decimals.
Step-by-step explanation:
To calculate the mass percent of water in the hydrated salt, we need to know the molar mass of water and the molar mass of the hydrated salt. Given that the molar mass of water (H2O) is approximately 18.015 g/mol, we can determine the total mass of 8 moles of water by multiplying this number by 8. This gives us 8 * 18.015 g/mol = 144.12 g/mol. The molar mass of the hydrated salt is then the sum of the molar mass of the anhydrous salt and the mass of the 8 moles of water, which is 160.167 g/mol + 144.12 g/mol = 304.287 g/mol.
Next, we calculate the percent by mass of water in the hydrated salt:
Percent by mass of water = (mass of water / mass of hydrated salt) * 100%
Percent by mass of water = (144.12 g/mol / 304.287 g/mol) * 100%
Percent by mass of water = 47.358%
Rounded to three decimal places, the mass percent of water in the hydrated salt is 47.358%.