What is the gram formula mass (molar mass) of lithium sulfate, Li2SO4, to three decimal places?

Introduction / Context:
Calculating gram formula mass, also called molar mass, is a routine yet vital skill in chemistry. It allows conversion between moles and grams and is used in stoichiometric calculations for reactions. This question asks for the gram formula mass of lithium sulfate, Li2SO4, to three decimal places. It tests accurate use of atomic masses and correct multiplication by the number of each type of atom in the formula.

Given Data / Assumptions:
- The compound is lithium sulfate with formula Li2SO4.
- Lithium has an atomic mass of approximately 6.941 u.
- Sulfur has an atomic mass of approximately 32.066 u.
- Oxygen has an atomic mass of approximately 15.999 u.
- We assume standard periodic table values and sum the contributions of all atoms in the formula.

Concept / Approach:
The gram formula mass of a compound is found by summing the atomic masses of all atoms present in one formula unit. For Li2SO4, there are two lithium atoms, one sulfur atom and four oxygen atoms. The calculation is: molar mass equals 2 times atomic mass of lithium plus 1 times atomic mass of sulfur plus 4 times atomic mass of oxygen. Careful multiplication and addition are needed, and the final result is usually rounded to appropriate significant figures, here given to four decimal places in the options.

Step-by-Step Solution:
Step 1: Multiply lithium's atomic mass by the number of lithium atoms: 2 * 6.941 = 13.882. Step 2: Take sulfur's atomic mass for one sulfur atom: 32.066. Step 3: Multiply oxygen's atomic mass by the number of oxygen atoms: 4 * 15.999 = 63.996. Step 4: Add these contributions: 13.882 + 32.066 + 63.996 = 109.944. Step 5: Compare this result with the given options and select the closest value, which is 109.9446 g/mol.

Verification / Alternative check:
As a check, one can approximate atomic masses to fewer decimal places and see if the result is close. Using 7 for lithium, 32 for sulfur and 16 for oxygen, the approximate calculation is 2 * 7 + 32 + 4 * 16, which equals 14 + 32 + 64 = 110 g/mol. This rough estimate is very close to the more precise 109.9446 g/mol given in the options. Since 109.9446 g/mol differs from the approximate 110 by only about 0.0554, whereas the other options differ more significantly, it is clear that 109.9446 g/mol is the most accurate value.

Why Other Options Are Wrong:
Option A, 101.2487 g/mol, is significantly lower than the expected approximate 110 g/mol and does not match the sum of atomic masses. Option C, 111.2687 g/mol, is higher than the calculated value and suggests an overestimation of one or more atomic contributions. Option D, 106.5871 g/mol, also deviates from both the precise and approximate calculations. None of these values match the carefully computed total based on standard atomic masses for Li2SO4.

Common Pitfalls:
A common mistake is miscounting the number of atoms in the formula, for example forgetting that there are two lithium atoms or four oxygen atoms. Another pitfall is rounding atomic masses too early in the calculation, which can introduce error. Students may also confuse gram formula mass with formula units or treat subscripts incorrectly. To avoid these issues, it is helpful to write down the contribution of each type of atom separately, multiply by its subscript and then sum everything at the end.

Final Answer:
The gram formula mass of lithium sulfate, Li2SO4, is 109.9446 g/mol.