Question

A chemical experiment was carried out at a temperature of 20°C. If the temperature was increased by 10°C, the time taken for the chemical reaction to occur would be 3 minutes faster. Given that the time taken for the chemical reaction to occur is inversely proportional to the temperature, how much should the temperature be increased by in order for the chemical reaction to occur 5 minutes faster?

Answer 1

`16.67`°
`C`

Explanation:

T = 20°
`C`

t = t minutes

---

When the temperature is increased by
`10`°
`C`, the time taken for the reaction to occur is 3 minutes faster. So, at the new temperature T +
`10`°
`C`, the time is
`t` -
`3` minutes. We can set up a proportion:

`(t)/(T)` =
`(t - 3)/(T + 10)`

Now, we can solve for
`t`:

`(t)/(20)` =
`(t - 3)/(30)`

To get rid of the fractions, you can cross-multiply:

`30t` =
`20t - 60`

`10t` =
`60`

`t` =
`6`

So, the initial time (
`t`) is
`6` minutes.

Now to find how much the temperature should be increased for the reaction to occur 5 minutes faster, we can set up a new proportion:

`(t)/(T)` =
`(t - 5)/(T+ΔT)`

Now, solve for Δ
`T`:

`(6)/(20)` =
`(1)/(20+ΔT)`

Cross-multiply:

`6(20 +`Δ
`T`

`120 + 6`Δ
`T` =
`20`

`6`Δ
`T` =
`20 - 120`

`6`Δ
`T` =
`-100`

Now, solve for Δ
`T`:

Δ
`T` =
`(-100)/(6)` =
`(-50)/(3)`

So, the temperature should be increaed by approximately
`-16.67`°
`C` for the chemical reaction to occur
`5` minutes faster. However, since temperature increase cannot be negative, this means you need to increase the temperature by
`16.67`°
`C` (approximately) for the reaction to occur 5 minutes faster.