if you added 4ml NaOH 1M to your 100ml 0.1M buffer, would it still be a usable buffer according to our convention? Explain why or why not(math would be good at here)
To determine if the resulting solution would still be a usable buffer, we need to analyze the changes in concentration of the buffer components (the acid and its conjugate base) in relation to the addition of NaOH.
Let's start by calculating the moles of the buffer components initially present in the 100 ml of 0.1 M buffer:
Moles of acid (HA) initially = initial volume (L) × initial concentration (mol/L)
= 0.1 L × 0.1 mol/L = 0.01 moles
Moles of conjugate base (A-) initially = initial volume (L) × initial concentration (mol/L)
= 0.1 L × 0.1 mol/L = 0.01 moles
Now, we need to determine the effect of adding 4 ml of 1 M NaOH to the buffer solution. NaOH is a strong base and reacts with the acidic component of the buffer (HA) to form its conjugate base (A-) and water. The reaction is as follows:
HA + NaOH → A- + H2O
The moles of acid (HA) remaining after the reaction can be calculated using the balanced stoichiometric coefficients of the equation:
Moles of acid (HA) remaining = initial moles of acid (HA) - moles of NaOH added
Since we added 4 ml or 0.004 L of 1 M NaOH, the moles of NaOH added can be calculated as follows:
Moles of NaOH added = volume added (L) × concentration of NaOH (mol/L)
= 0.004 L × 1 mol/L = 0.004 moles
Therefore, the moles of acid (HA) remaining after the reaction are:
Moles of acid (HA) remaining = 0.01 moles - 0.004 moles = 0.006 moles
Similarly, the moles of the conjugate base (A-) formed can be determined from the stoichiometric coefficients:
Moles of conjugate base (A-) formed = moles of NaOH added
= 0.004 moles
Now we can calculate the concentrations of the remaining acid (HA) and formed conjugate base (A-) in the final volume of the solution (104 ml) after the addition of NaOH:
Concentration of acid (HA) = moles of acid (HA) remaining / final volume (L)
= 0.006 moles / 0.104 L = 0.0577 M
Concentration of conjugate base (A-) = moles of conjugate base (A-) formed / final volume (L)
= 0.004 moles / 0.104 L = 0.0385 M
To determine if the resulting solution is still a usable buffer, we need to compare the concentrations of the acid (HA) and its conjugate base (A-). According to the convention, a buffer is effective when the ratio of the concentrations of the conjugate base to the acid, known as the buffer capacity (β), lies between 0.1 and 10.
Calculating the buffer capacity:
β = concentration of conjugate base (A-) / concentration of acid (HA)
= 0.0385 M / 0.0577 M ≈ 0.668
In this case, the resulting buffer has a buffer capacity of approximately 0.668, which falls within the range of 0.1 to 10. Therefore, the resulting solution would still be a usable buffer according to our convention.
Note: It is important to note that this calculation assumes ideal behavior and does not consider any additional factors that may affect the buffer capacity, such as the pKa of the acid.