Final answer:
To prepare a 1.00 L pH 3.00 buffer with a total concentration of 0.200 M, you would need 27.628 g of bromoacetic acid and 5.460 g of sodium bromoacetate.
Step-by-step explanation:
To calculate the masses of bromoacetic acid and sodium bromoacetate needed to prepare a 1.00 L pH 3.00 buffer with a total concentration of 0.200 M, we need to use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is: pH = pKa + log([A-]/[HA]).
First, we need to find the pKa value. Since bromoacetic acid is a weak acid, we can assume that its pKa value is similar to acetic acid, which is 4.74.
Using the Henderson-Hasselbalch equation, we can rearrange it to find [A-]/[HA]. [A-]/[HA] = 10^(pH - pKa).
Since we want a pH of 3.00, [A-]/[HA] = 10^(3.00 - 4.74) = 0.211.
Next, we can set up an equation using the total concentration of the two components. Let x be the concentration of bromoacetic acid, so the concentration of sodium bromoacetate will be 0.200 - x.
Using the equation [A-]/[HA] = 0.211, we can substitute in the concentrations: (0.200 - x)/x = 0.211.
Simplifying this equation, we get 0.200 - x = 0.211x. Rearranging, we have 0.211x + x = 0.200, which gives us 1.211x = 0.200.
Solving for x, we find that x = 0.165 M. So the concentration of bromoacetic acid is 0.165 M and the concentration of sodium bromoacetate is 0.200 - 0.165 = 0.035 M.
To calculate the masses of the two components, we need to convert the molar concentrations to moles. The moles of bromoacetic acid is equal to the concentration (in M) multiplied by the volume (in L): 0.165 mol/L x 1.00 L = 0.165 mol.
The mass of bromoacetic acid can be calculated by multiplying the moles by the molar mass: 0.165 mol x 167.96 g/mol = 27.628 g.
The moles of sodium bromoacetate is equal to the concentration (in M) multiplied by the volume (in L): 0.035 mol/L x 1.00 L = 0.035 mol.
The mass of sodium bromoacetate can be calculated by multiplying the moles by the molar mass: 0.035 mol x 156.01 g/mol = 5.460 g.
Therefore, to prepare 1.00 L of a pH 3.00 buffer with a total concentration of 0.200 M, you would need 27.628 g of bromoacetic acid and 5.460 g of sodium bromoacetate.