Answer
The molecular mass of \( \mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2} \cdot 5 \mathrm{H}_{2} \mathrm{O} \) is **236.4 g/mol**.
Solution
Calculate the value by following steps:
- step0: Calculate:
\(24.305+2\left(1.00784+12.0107+3\times 15.999\right)+5\left(2\times 1.00784+15.999\right)\)
- step1: Multiply the numbers:
\(24.305+2\left(1.00784+12.0107+47.997\right)+5\left(2\times 1.00784+15.999\right)\)
- step2: Add the numbers:
\(24.305+2\times 61.01554+5\left(2\times 1.00784+15.999\right)\)
- step3: Multiply the numbers:
\(24.305+2\times 61.01554+5\left(2.01568+15.999\right)\)
- step4: Add the numbers:
\(24.305+2\times 61.01554+5\times 18.01468\)
- step5: Multiply the numbers:
\(24.305+122.03108+5\times 18.01468\)
- step6: Multiply the numbers:
\(24.305+122.03108+90.0734\)
- step7: Add the numbers:
\(236.40948\)
Round the number \( 236.40948 \) into 1 decimal place.
Round the number by following steps:
- step0: Round \(236.40948\) to \(1\) decimal places using standard rounding method:
\(236.40948\)
- step1: Round \(236.40948\) to \(1\) decimal places using standard rounding method\(:\)
\(236.4\)
To calculate the molecular mass of \( \mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2} \cdot 5 \mathrm{H}_{2} \mathrm{O} \), we need to sum the atomic masses of all the atoms in the formula.
1. **Calculate the mass of \( \mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2} \)**:
- Magnesium (Mg): 1 atom × 24.305 g/mol = 24.305 g/mol
- Hydrogen (H): 2 atoms × 1.00784 g/mol = 2.01568 g/mol
- Carbon (C): 2 atoms × 12.0107 g/mol = 24.0214 g/mol
- Oxygen (O): 6 atoms × 15.999 g/mol = 95.994 g/mol
Adding these together:
\[
24.305 + 2.01568 + 24.0214 + 95.994 = 146.33608 \text{ g/mol}
\]
2. **Calculate the mass of \( 5 \mathrm{H}_{2} \mathrm{O} \)**:
- Hydrogen (H): 10 atoms × 1.00784 g/mol = 10.0784 g/mol
- Oxygen (O): 5 atoms × 15.999 g/mol = 79.995 g/mol
Adding these together:
\[
10.0784 + 79.995 = 90.0734 \text{ g/mol}
\]
3. **Total molecular mass**:
\[
146.33608 + 90.0734 = 236.40948 \text{ g/mol}
\]
Rounding this to 1 decimal place gives us:
\[
\text{Molecular mass} = 236.4 \text{ g/mol}
\]
Thus, the molecular mass of \( \mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2} \cdot 5 \mathrm{H}_{2} \mathrm{O} \) is **236.4 g/mol**.
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