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A drop of solution (volume 0.05 mL) contains 3.0 x 10-6 mole of H+. If the rate constant of disappearance of H+ is 1.0 x 10-7 mol litre-1 sec-1. How long would it take for H+ in drop to disappear?
 
  • a)
        6 x 10-8 sec    
  • b)
        6 x 10-7        
  • c)
        6 x 10-9 sec    
  • d)
        6 x 10-10 sec
Correct answer is option 'C'. Can you explain this answer?
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A drop of solution (volume 0.05 mL) contains 3.0 x 10-6 mole of H+. If...
Since rate constant = 1 x 10-7 mol litre-1 sec-1 
         ∴   Zero order reaction
0.05 mL has 3 x 10-6 mole of H+
 
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A drop of solution (volume 0.05 mL) contains 3.0 x 10-6 mole of H+. If...
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A drop of solution (volume 0.05 mL) contains 3.0 x 10-6 mole of H+. If...
To determine how long it would take for the H in the drop to disappear, we can use the first-order rate equation:

Rate = k[H]

Where:
- Rate is the rate of disappearance of H (in mol L-1 sec-1)
- k is the rate constant (in mol L-1 sec-1)
- [H] is the concentration of H (in mol L-1)

We are given the volume of the solution (0.05 mL) and the number of moles of H (3.0 x 10-6 mol). We can use these values to calculate the concentration of H:

[H] = moles of H / volume of solution

[H] = (3.0 x 10-6 mol) / (0.05 mL) = 6.0 x 10-5 mol L-1

Now we can substitute the values into the rate equation:

Rate = (1.0 x 10-7 mol L-1 sec-1)(6.0 x 10-5 mol L-1)

Rate = 6.0 x 10-12 mol sec-1

The rate of disappearance of H is 6.0 x 10-12 mol sec-1.

To find the time it would take for the H in the drop to disappear, we can rearrange the rate equation:

Rate = k[H]

t = 1 / (k[H])

t = 1 / ((1.0 x 10-7 mol L-1 sec-1)(6.0 x 10-5 mol L-1))

t = 1 / (6.0 x 10-12 mol sec-1)

t = 1.67 x 1011 sec

Converting this time to scientific notation, we get:

t ≈ 1.67 x 1011 sec = 1.67 x 1011 sec x 10-9 sec = 1.67 x 102 sec x 10-9 sec = 1.67 x 10-7 sec

Therefore, it would take approximately 1.67 x 10-7 seconds for the H in the drop to disappear. This is equivalent to 6 x 10-9 seconds, which matches option C.
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A drop of solution (volume 0.05 mL) contains 3.0 x 10-6 mole of H+. If the rate constant of disappearance of H+ is 1.0 x 10-7 mol litre-1 sec-1. How long would it take for H+ in drop to disappear?a) 6 x 10-8 sec b) 6 x 10-7 c) 6 x 10-9 sec d) 6 x 10-10 secCorrect answer is option 'C'. Can you explain this answer?
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