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NCERT Exemplar · Q10

Q.For the same plot of the volume of hydrogen collected against time in the zinc + dilute HCl reaction (a curve through the origin, with volumes V1,V2,V3,V4V_1, V_2, V_3, V_4 read on the curve at t=20,30,40,50 st=20, 30, 40, 50\text{ s} respectively, and V5V_5 the value at t=50 st=50\text{ s} read off the straight tangent drawn to the curve at t=40 st=40\text{ s}), identify the expression that does NOT represent the instantaneous rate of reaction at the 40th second.

(i) V5−V250−30\dfrac{V_5 - V_2}{50 - 30}
(ii) V4−V250−30\dfrac{V_4 - V_2}{50 - 30}
(iii) V3−V240−30\dfrac{V_3 - V_2}{40 - 30}
(iv) V3−V140−20\dfrac{V_3 - V_1}{40 - 20}
Telangana TsbieMCQ· 1mImportance★★★★★
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The instantaneous rate at 40 s is the slope of the tangent to the curve at t=40 st=40\text{ s}, best estimated from a small interval centred on (or ending at) 40 s. Options (i), (ii) and (iii) all do that; option (iv) uses the interval 20-40 s20\text{-}40\text{ s}, centred on 30 s, so it gives the average rate near 30 s rather than the instantaneous rate at 40 s.

Concept

Instantaneous rate at a time tt = slope of the tangent to the volume-time curve at tt. Numerically it is approximated by ΔVΔt\frac{\Delta V}{\Delta t} over a small interval placed at that time.

Testing each option

  • (i) V5−V250−30\frac{V_5-V_2}{50-30}: interval 30-50 s30\text{-}50\text{ s}, symmetric about 40 s and using the tangent value V5V_5 at 50 s - represents the tangent slope at 40 s. Shows it.
  • (ii) V4−V250−30\frac{V_4-V_2}{50-30}: interval 30-50 s30\text{-}50\text{ s}, a central difference on the curve - a good estimate of the rate at 40 s. Shows it. …

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