Question

A solution contains 31.0 grams of glutamic acid, C₅H₉NO₄, in a total solution volume of 0.560 L. What is the concentration of glutamic acid in the solution?

a) 8.47 M
b) 0.118 M
c) 0.376 M
d) 55.4 M
e) 0.211 M

Answer 1

To calculate the concentration of glutamic acid in the solution, convert the mass of glutamic acid to moles using its molar mass (147.13 g/mol) and then divide by the volume of the solution (0.560 L) to find the molarity, which is approximately 0.376 M.

Step-by-step explanation:

The concentration of glutamic acid in the solution can be calculated using the formula for molarity, which is moles of solute divided by liters of solution. First, we need to convert the mass of glutamic acid into moles by using its molar mass. The molar mass of glutamic acid (C5H9NO4) is the sum of the molar masses of its constituent atoms: 5(12.01 g/mol) for carbon, 9(1.008 g/mol) for hydrogen, 1(14.01 g/mol) for nitrogen, and 4(16.00 g/mol) for oxygen, totaling to approximately 147.13 g/mol. Divide the mass of glutamic acid by its molar mass to find the number of moles:

• molar mass of glutamic acid = 5(12.01) + 9(1.008) + 1(14.01) + 4(16.00) = 147.13 g/mol
• moles of glutamic acid = 31.0 g / 147.13 g/mol ≈ 0.2107 moles

Next, divide the moles of glutamic acid by the volume of the solution to find the molarity:

• molarity = moles of solute / liters of solution
• molarity = 0.2107 moles / 0.560 L ≈ 0.376 M

Therefore, the concentration of glutamic acid in the solution is 0.376 M.