Calculate the mass of 5.3 moles of chloric acid (HClO₃).
Explain the process or show your work by including all values used to determine the answer.
The Correct Answer and Explanation is :
To calculate the mass of 5.3 moles of chloric acid (( \text{HClO}_3 )), we use the molar mass of the compound and the formula:
[
\text{Mass} = \text{Moles} \times \text{Molar Mass}
]
Step 1: Determine the molar mass of HClO₃
We calculate the molar mass by adding the atomic masses of hydrogen (H), chlorine (Cl), and oxygen (O). The atomic masses are approximately:
- Hydrogen (H): 1.01 g/mol
- Chlorine (Cl): 35.45 g/mol
- Oxygen (O): 16.00 g/mol
Since ( \text{HClO}_3 ) has one hydrogen, one chlorine, and three oxygens, we calculate the molar mass as follows:
[
1.01 \, \text{g/mol} + 35.45 \, \text{g/mol} + (3 \times 16.00 \, \text{g/mol}) = 1.01 + 35.45 + 48.00 = 84.46 \, \text{g/mol}
]
Thus, the molar mass of HClO₃ is 84.46 g/mol.
Step 2: Calculate the mass of 5.3 moles of HClO₃
Now, we use the formula with the molar mass and the number of moles:
[
\text{Mass} = 5.3 \, \text{moles} \times 84.46 \, \text{g/mol} = 447.638 \, \text{g}
]
Rounding to three significant figures, the mass is approximately:
[
\text{Mass} \approx 448 \, \text{g}
]
Explanation
In this calculation, the molar mass acts as a conversion factor between moles and grams. Knowing that each mole of HClO₃ has a mass of 84.46 grams, we simply multiply by the number of moles (5.3) to find the total mass. This process of dimensional analysis allows us to convert moles to grams easily when the molar mass is known. The result, 448 grams, represents the total mass of 5.3 moles of chloric acid. This method is fundamental in chemistry and is widely used for calculating masses in stoichiometric problems, where we need to determine the mass of a substance given its amount in moles.