Monosodium glutamate (MSG), a food-flavor enhancer, has been blamed for “Chinese Restaurant Syndrome,” the symptoms of which are headaches & chest pains. MSG has the following composition by mass: 35.51 percent C, 4.77 percent H, 37.85 percent O, 8.29 percent N, & 13.60 percent Na. What is its molecular formula if its molar mass is about 169 g?
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To determine the molecular formula of monosodium glutamate (MSG) given its composition by mass, we need to calculate the empirical formula and then find the molecular formula.
Step 1: Convert mass percentages to grams for each element
- Carbon (C): 35.51% of 169 g = 60.01 g
- Hydrogen (H): 4.77% of 169 g = 8.07 g
- Oxygen (O): 37.85% of 169 g = 63.99 g
- Nitrogen (N): 8.29% of 169 g = 14.01 g
- Sodium (Na): 13.60% of 169 g = 22.98 g
Step 2: Convert grams to moles for each element
- Carbon (C): 60.01 g / atomic mass of C = 60.01 g / 12.01 g/mol ≈ 5.00 moles
- Hydrogen (H): 8.07 g / atomic mass of H = 8.07 g / 1.01 g/mol ≈ 8.00 moles
- Oxygen (O): 63.99 g / atomic mass of O = 63.99 g / 16.00 g/mol ≈ 4.00 moles
- Nitrogen (N): 14.01 g / atomic mass of N = 14.01 g / 14.01 g/mol ≈ 1.00 moles
- Sodium (Na): 22.98 g / atomic mass of Na = 22.98 g / 22.99 g/mol ≈ 1.00 moles
Step 3: Divide the number of moles by the smallest number of moles obtained. In this case, Nitrogen has the lowest number of moles, which is 1.00 mole. Divide all other moles by 1.00 mole.
- Carbon (C): 5.00 moles / 1.00 moles = 5.00
- Hydrogen (H): 8.00 moles / 1.00 moles = 8.00
- Oxygen (O): 4.00 moles / 1.00 moles = 4.00
- Nitrogen (N): 1.00 mole / 1.00 mole = 1.00
- Sodium (Na): 1.00 mole / 1.00 mole = 1.00
Step 4: Obtain the empirical formula from the resulting ratios.
The empirical formula for MSG is C5H8NO4Na.
To find the molecular formula, we need to determine the ratio between the empirical formula weight and the molar mass provided.
Step 5: Calculate the empirical formula weight.
- Carbon (C): 5.00 moles x atomic mass of C = 5.00 moles x 12.01 g/mol = 60.05 g
- Hydrogen (H): 8.00 moles x atomic mass of H = 8.00 moles x 1.01 g/mol = 8.08 g
- Oxygen (O): 4.00 moles x atomic mass of O = 4.00 moles x 16.00 g/mol = 64.00 g
- Nitrogen (N): 1.00 mole x atomic mass of N = 1.00 mole x 14.01 g/mol = 14.01 g
- Sodium (Na): 1.00 mole x atomic mass of Na = 1.00 mole x 22.99 g/mol = 22.99 g
Empirical formula weight: 60.05 g + 8.08 g + 64.00 g + 14.01 g + 22.99 g = 169.13 g
Step 6: Divide the molar mass (169 g) by the empirical formula weight (169.13 g) to obtain the ratio.
169 g / 169.13 g = 0.999
Step 7: Multiply the empirical formula by the ratio obtained.
C5H8NO4Na x 0.999 ≈ C5H8NO4Na
Therefore, the molecular formula of MSG is C5H8NO4Na.
Please note that the molar mass provided is approximately 169 g, so the resulting molecular formula is also an approximation.
To determine the molecular formula of monosodium glutamate (MSG), we need to find the empirical formula first and then calculate the molecular formula using the molar mass provided.
Step 1: Calculate the empirical formula.
The empirical formula represents the simplest whole-number ratio of atoms in a compound. To calculate it, we need to find the moles of each element present in MSG.
Given composition by mass:
C: 35.51%
H: 4.77%
O: 37.85%
N: 8.29%
Na: 13.60%
Based on these percentages, we can assume we have 100g of MSG. Therefore, we can convert the mass percentages to grams.
C: 35.51g (35.51% of 100g)
H: 4.77g (4.77% of 100g)
O: 37.85g (37.85% of 100g)
N: 8.29g (8.29% of 100g)
Na: 13.60g (13.60% of 100g)
Next, we need to find the moles of each element by dividing the given grams by their respective molar masses.
Molar masses:
C: 12.01 g/mol
H: 1.01 g/mol
O: 16.00 g/mol
N: 14.01 g/mol
Na: 22.99 g/mol
Moles of each element:
C: 35.51g / 12.01 g/mol ≈ 2.96 mol
H: 4.77g / 1.01 g/mol ≈ 4.72 mol
O: 37.85g / 16.00 g/mol ≈ 2.36 mol
N: 8.29g / 14.01 g/mol ≈ 0.59 mol
Na: 13.60g / 22.99 g/mol ≈ 0.59 mol
Next, we need to find the simplest whole-number ratio of moles by dividing each number of moles by the smallest number of moles (in this case, 0.59 mol).
Dividing by 0.59 mol:
C: 2.96 mol / 0.59 mol ≈ 5
H: 4.72 mol / 0.59 mol ≈ 8
O: 2.36 mol / 0.59 mol ≈ 4
N: 0.59 mol / 0.59 mol = 1
Na: 0.59 mol / 0.59 mol = 1
The empirical formula of MSG based on these ratios is C5H8NO4Na.
Step 2: Calculate the molecular formula.
To determine the molecular formula, we need to know the molar mass of the compound. The given molar mass for MSG is approximately 169 g/mol.
Next, we need to calculate the empirical formula mass, which is the sum of the atomic masses in the empirical formula.
Empirical formula mass:
C: 12.01 g/mol x 5 = 60.05 g/mol
H: 1.01 g/mol x 8 = 8.08 g/mol
O: 16.00 g/mol x 4 = 64.00 g/mol
N: 14.01 g/mol x 1 = 14.01 g/mol
Na: 22.99 g/mol x 1 = 22.99 g/mol
Sum of empirical formula mass:
60.05 g/mol + 8.08 g/mol + 64.00 g/mol + 14.01 g/mol + 22.99 g/mol = 169.13 g/mol
Since the molar mass of MSG given is approximately 169 g/mol, which is very close to the empirical formula mass calculated above, the empirical formula (C5H8NO4Na) is also the molecular formula.
Therefore, the molecular formula of MSG is C5H8NO4Na.