Monosodium glutamate (aka MSG) NaC5H8NO4 is used as a food additive for flavor or as a preservative.
a. what is the mass of MSG (g) that contains 545 mg sodium?
b. calculate the percentage of each element present in MSG.
a. To find the mass of MSG that contains 545 mg of sodium, we need to consider the molar mass of MSG and use stoichiometry.
The molar mass of MSG (NaC5H8NO4) can be calculated by adding up the atomic masses of each element present in MSG. The atomic masses (in g/mol) are as follows:
Na (sodium): 22.99 g/mol
C (carbon): 12.01 g/mol
H (hydrogen): 1.01 g/mol
N (nitrogen): 14.01 g/mol
O (oxygen): 16.00 g/mol
To calculate the molar mass of MSG:
molar mass of MSG = (sodium atomic mass) + (carbon atomic mass * 5) + (hydrogen atomic mass * 8) + (nitrogen atomic mass) + (oxygen atomic mass * 4)
molar mass of MSG = (22.99 g/mol) + (12.01 g/mol * 5) + (1.01 g/mol * 8) + (14.01 g/mol) + (16.00 g/mol * 4)
molar mass of MSG ≈ 169.12 g/mol
Now, we can set up the stoichiometric relationship between the mass of sodium and the molar mass of MSG:
mass of sodium / molar mass of MSG = mass of MSG
mass of MSG = (mass of sodium / molar mass of MSG)
mass of MSG = (545 mg / 1000 mg/g) * (1 g/1000 mg) * (169.12 g/mol)
mass of MSG ≈ 0.092 g
Therefore, the mass of MSG that contains 545 mg of sodium is approximately 0.092 grams.
b. To calculate the percentage of each element present in MSG, we need to determine the molar mass of each element and the total molar mass of MSG.
We have already calculated the molar mass of MSG, which is approximately 169.12 g/mol.
Now, we need to find the molar mass of each element:
- Sodium (Na): 22.99 g/mol
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Nitrogen (N): 14.01 g/mol
- Oxygen (O): 16.00 g/mol
To calculate the percentage of each element in MSG, we divide the molar mass of each element by the total molar mass of MSG and multiply by 100:
Percentage of Sodium = (Na molar mass / MSG molar mass) * 100
Percentage of Carbon = (C molar mass / MSG molar mass) * 100
Percentage of Hydrogen = (H molar mass / MSG molar mass) * 100
Percentage of Nitrogen = (N molar mass / MSG molar mass) * 100
Percentage of Oxygen = (O molar mass / MSG molar mass) * 100
Percentage of Sodium = (22.99 g/mol / 169.12 g/mol) * 100
Percentage of Carbon = (12.01 g/mol / 169.12 g/mol) * 100
Percentage of Hydrogen = (1.01 g/mol / 169.12 g/mol) * 100
Percentage of Nitrogen = (14.01 g/mol / 169.12 g/mol) * 100
Percentage of Oxygen = (16.00 g/mol / 169.12 g/mol) * 100
After calculating these percentages, we will have the percentage composition of each element in MSG.
a. To find the mass of MSG that contains 545 mg of sodium, we need to determine the molar mass of MSG and use it to calculate the mass of sodium.
The molar mass of MSG (NaC5H8NO4) can be calculated by adding up the atomic masses of all its elements. Here are the atomic masses of the elements involved:
- Sodium (Na): 22.99 g/mol
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Nitrogen (N): 14.01 g/mol
- Oxygen (O): 16.00 g/mol
Now, let's calculate the molar mass of MSG:
Molar mass of MSG = (1 x Na) + (5 x C) + (8 x H) + (1 x N) + (4 x O)
= (1 x 22.99) + (5 x 12.01) + (8 x 1.01) + (1 x 14.01) + (4 x 16.00)
= 22.99 + 60.05 + 8.08 + 14.01 + 64.00
= 169.13 g/mol
To find the mass of MSG that contains 545 mg of sodium, we can use the following formula:
Mass of MSG = (mass of sodium / molar mass of MSG) x molar mass of MSG
Mass of MSG = (545 mg / 1000) x 169.13 g/mol
= 0.545 g x 169.13 g/mol
= 92.27 g
Therefore, the mass of MSG that contains 545 mg of sodium is 92.27 grams.
b. To calculate the percentages of each element present in MSG, we need to determine the molar masses of each individual element and divide them by the molar mass of MSG. Then, we can multiply by 100 to find the percentage.
Molar mass of sodium (Na) = 22.99 g/mol
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
Molar mass of nitrogen (N) = 14.01 g/mol
Molar mass of oxygen (O) = 16.00 g/mol
Now, we can calculate the percentages of each element in MSG:
Percentage of sodium = (mass of sodium / molar mass of MSG) x 100
= (22.99 g / 169.13 g/mol) x 100
≈ 13.61%
Percentage of carbon = (5 x molar mass of carbon / molar mass of MSG) x 100
= (5 x 12.01 g/mol / 169.13 g/mol) x 100
≈ 35.56%
Percentage of hydrogen = (8 x molar mass of hydrogen / molar mass of MSG) x 100
= (8 x 1.01 g/mol / 169.13 g/mol) x 100
≈ 4.76%
Percentage of nitrogen = (molar mass of nitrogen / molar mass of MSG) x 100
= (14.01 g/mol / 169.13 g/mol) x 100
≈ 8.28%
Percentage of oxygen = (4 x molar mass of oxygen / molar mass of MSG) x 100
= (4 x 16.00 g/mol / 169.13 g/mol) x 100
≈ 37.79%
Therefore, the percentages of each element present in MSG are approximately:
- Sodium: 13.61%
- Carbon: 35.56%
- Hydrogen: 4.76%
- Nitrogen: 8.28%
- Oxygen: 37.79%