500 ml of a buffer solution with ph=2.10 must be prepared using .4 M HNO2 and solid KNO2. The ka value of HNO2 is 4e-3.

a.) What mass of KNO2 should be added to 3 L of the HNO2 to make the buffer?
b.) What is the buffer's pH after 150 ml of .5 M HNO3 is added?

Approx means I've estimated. You should go through yourself and get good answers.

pKa = approx 2.4
mols HNO2 = 0.5L x 0.4M = 0.2 = acid
pH = pKa + log (base)/(acid)
2.10 = 2.40 + log (x/0.2)
Solve for x = mols KNO2 = about 0.1 mol = ? grams.

b.
millimols HNO2 = 500 mL x 0.4M = 200
mmols HNO3 added = 150 x 0.5M = 75
mmols KBNO2 = 100 from above.

............NO2^- + H^+ ==> HNO2
I.......... 100......0.......200
added........0......75........0
C...........-75.....-75.......+75
E............25......0........275

Plug that E line (after you've recalculated everything to get the good numbers to use) into HH equation and solve for pH.

To answer these questions, we need to understand how buffers work and how pH is calculated in buffer solutions.

A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added to it. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). In this case, the weak acid is HNO2 and its conjugate base is NO2-.

Now, let's tackle each question step by step:

a.) What mass of KNO2 should be added to 3 L of the HNO2 to make the buffer?

To prepare the buffer, we need to determine the moles of HNO2 required and then use the balanced equation to calculate the moles of KNO2 needed. Finally, we'll convert the moles of KNO2 to mass.

1. Calculate the moles of HNO2 required:
Given:
Volume of HNO2 = 3 L
Concentration of HNO2 = 0.4 M

Moles of HNO2 = Concentration x Volume
Moles of HNO2 = 0.4 M x 3 L

2. Calculate the moles of KNO2 required using the balanced equation:
The balanced equation for the reaction between HNO2 and KNO2 is:

HNO2 + KNO2 ↔ HNO2 + KNO2

From the equation, we see that the moles of KNO2 required are equal to the moles of HNO2.

3. Convert the moles of KNO2 to mass:
To convert moles to mass, we'll need the molar mass of KNO2. The molar mass of KNO2 is the sum of the atomic masses of potassium (K), nitrogen (N), and two oxygen (O) atoms.

Finally, use the formula: Mass = Moles x Molar Mass

b.) What is the buffer's pH after 150 ml of 0.5 M HNO3 is added?

To determine the change in pH after adding 150 ml of 0.5 M HNO3, we need to consider the reaction between HNO2 and HNO3.

The balanced equation for the reaction between HNO2 and HNO3 is:

HNO2 + HNO3 ↔ H2O + NO2+ (conjugate acid of HNO2) + NO3- (conjugate base of HNO3)

Given:
Volume of HNO3 = 150 ml = 0.15 L
Concentration of HNO3 = 0.5 M

We can use the Henderson-Hasselbalch equation to calculate the new pH of the buffer solution after the addition of HNO3:

pH = pKa + log ([conjugate base]/[weak acid])

To solve this equation, we need to know the initial concentration of the weak acid (HNO2) and its conjugate base (NO2-). The initial concentration of HNO2 can be calculated using the volume and concentration of HNO2, while the initial concentration of NO2- can be determined by the amount of KNO2 added.

Once we have the initial concentrations, we can calculate the final concentrations of both the weak acid and its conjugate base by taking into account the reaction with HNO3 and the volume change.

Finally, substitute the values into the Henderson-Hasselbalch equation to find the new pH.

Note: The Henderson-Hasselbalch equation assumes the buffer capacity is not exceeded, meaning that the change in pH is within the effective buffering range. If the added acid or base exceeds the buffer capacity, the pH change becomes more significant and other calculations are needed.