An aqueous solution contains 0.01 M RNH2(Kb= 2 × 10-6) & 10-4...


x
2 + 10
–4 x – 2 × 10
–8 = 0
x = 10
–4[OH–] = x + 10
–4= 2 × 10
–4
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An aqueous solution contains 0.01 M RNH2(Kb= 2 × 10-6) & 10-4...
Given:
- Concentration of RNH2 (weak base) = 0.01 M
- Concentration of NaOH (strong base) = 10-4 M
- Kb (base dissociation constant) for RNH2 = 2 * 10-6
To find:
- Concentration of OH- in the solution
Formula:
- Kb = [OH-][RNH2]/[RNH3+]
Solution:
Step 1: Write down the balanced equation for the reaction between RNH2 and OH-:
RNH2 + OH- → RNH3+ + OH-
Step 2: Calculate the concentration of RNH3+ formed:
Since RNH2 is a weak base, it partially ionizes to form RNH3+ and OH-. Let x be the concentration of RNH3+ formed. Since the concentration of RNH2 is much greater than the concentration of OH-, we can assume that the amount of RNH2 reacting is not significantly changed, so the concentration of RNH3+ formed is approximately equal to x.
Step 3: Calculate the concentration of OH-:
Since the concentration of OH- formed is equal to the concentration of RNH3+ formed, we can write:
[OH-] = x
Step 4: Write the expression for Kb and substitute the known values:
Kb = [OH-][RNH2]/[RNH3+]
2 * 10-6 = x * 0.01 / x
Step 5: Solve for x:
Cross-multiplying the equation:
2 * 10-6 * x = x * 0.01
Simplifying the equation:
2 * 10-6 = 0.01
Dividing both sides by 2 * 10-6:
x = 0.01 / 2 * 10-6
x = 5 * 103
Therefore, the concentration of OH- is 5 * 10-3 M, which is equal to 2 * 10-4 M.
Hence, the correct answer is option D: 2 * 10-4 M.