Rate of a Reaction

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle before we start. Nitrogen and hydrogen join to make ammonia. In the flask, at one and the same moment, hydrogen is used up three times as fast as nitrogen, and ammonia forms twice as fast as nitrogen is used up. Three different speeds, for one single reaction! So, what is the rate of this reaction? Which speed do we pick? By the end of this video, you will find that a reaction has just one rate. Questions like this come up often in JEE, so let's begin.

0:38Average rate and instantaneous rate

So, the rate of a reaction is simply how fast the concentrations change with time. On screen is the average rate, over a time interval delta t. The little triangle is delta, and it means the change: final minus initial. And the square brackets mean concentration, in moles per litre, okay? So the average rate is delta of product concentration, over delta t. Now, what about a reactant? Its concentration goes down as the reaction runs. So the change, delta of reactant concentration: is it positive or negative? Negative, yes! The reactant is used up, so final minus initial is negative. But a rate should be a positive number, right? So for a reactant, we put a minus sign in front: minus delta of reactant concentration, over delta t. The minus sign keeps the rate positive. Clear? Now, the average rate covers a whole interval. But often we want the rate at one exact instant. Plot concentration against time, and you get a curve. The instantaneous rate is the slope of this concentration time curve, at that instant. For a reactant, the curve goes downward, so the slope is negative, and we take minus the slope. Okay? And we write it with a small d in place of delta: d of product concentration over d t, or minus d of reactant concentration over d t. The d tells you this is the rate at one instant, the slope at that point. With me?

2:14One rate for the whole reaction

Now, back to our puzzle. Take a general reaction: small a of capital A, plus small b of capital B, gives small c of capital C, plus small d of capital D, okay? The arrow means gives, and the small letters a, b, c and d are the coefficients in the balanced equation. Right? Each species changes at its own speed. So how can we get one single rate for the whole reaction? Divide each one by its coefficient! r, the rate of reaction, equals minus one over a, times d A over d t. Here d A over d t, with A in square brackets, is the rate of change of the concentration of A, at that instant. It also equals minus one over b, times d B over d t. Reactants get the minus sign, just like before. Okay? For the products, there is no minus sign: one over c, times d C over d t, and one over d, times d D over d t. Got it? Now here is the beauty of it. All four expressions give the same number r, whichever species you measure. So a reaction has only one rate. Okay? And here is a trap. The rate at which a product forms, d C over d t, equals the rate of reaction r only when its coefficient c is one. Otherwise you must divide by the coefficient. Careful with this one, right?

3:39Units, and what the rate depends on

Next, units. Rate is concentration over time. Concentration is in moles per litre, and time is in seconds. So, what are the units of rate? Moles per litre per second, correct! On screen: mol, short for moles, then L, for litre, to the power minus one, then s, for second, to the power minus one. Each power of minus one simply means per. Clear? For gases, the rate can also be given in pressure units: atm, short for atmospheres, per second, right? Finally, the rate depends on these factors. First, the concentration of the reactants, or the pressure for gases. Then the temperature, and catalysts. Okay? Then the surface area, and light, for photochemical reactions, the ones driven by light. Keep this list in mind. Got it?

4:34Example 1: rates of N2, H2 and NH3 in ammonia formation

Now, let's settle our puzzle. N two plus three H two gives two N H three. The small numbers written below the letters count the atoms: N two is nitrogen, H two is hydrogen, and N H three is ammonia, okay? Ammonia forms at zero point six moles per litre per minute. Find the rates at which nitrogen and hydrogen are used up, and the rate of reaction. Pause the video and try it first. Done? Okay, let's check. Ammonia forms at zero point six. So the rate of reaction is zero point six, right? No, no, careful here! Ammonia has a coefficient of two. So r equals one half, times d N H three over d t. Half of zero point six is zero point three. That is the rate of reaction. With me? Nitrogen has a coefficient of one, so it is used up at the rate r itself: minus d N two over d t equals zero point three. Clear? Now hydrogen, with a coefficient of three. How fast is it used up? Three times r: three times zero point three, that is zero point nine. Careful: it is three times r, not three times the zero point six of ammonia. That slip is very common. Okay? And all of these are in moles per litre per minute, because the time was in minutes. So look: three speeds, zero point three, zero point nine and zero point six, but just one rate of reaction, zero point three. Our puzzle is solved! Right?

6:13Example 2: N2O5 decomposition, rates of N2O5 and O2

Now a slightly harder one. Two N two O five gives four N O two plus O two. The concentration of N O two rises by zero point zero two four moles per litre in five seconds. Find the rate at which N two O five disappears, and the rate at which oxygen forms. Pause the video and try it first. Done? Okay, let's check. First, the rate at which N O two forms: the change over the time, zero point zero two four over five, which is four point eight times ten to the power minus three moles per litre per second. That is the average rate over these five seconds. Okay? Now compare the coefficients: two for N two O five, four for N O two, and one for oxygen. Two to four to one, as the colons on screen show. Right? So tell me: does N two O five disappear faster or slower than N O two forms? Slower, exactly! Its coefficient is two, against four. So its rate is two over four, that is half, of four point eight times ten to the power minus three. That gives two point four times ten to the power minus three. It is easy to flip this ratio and get double, so be careful here. And oxygen, with coefficient one: one quarter of four point eight times ten to the power minus three, which is one point two times ten to the power minus three. And see the r at the end: since the coefficient of oxygen is one, this is also the rate of reaction. Got it? Both answers are in moles per litre per second, because the time was in seconds. Always check the time unit. Clear?

7:59Quick revision: average, instantaneous rate and units

So, quick revision. The average rate is the change in concentration over the time interval, and the instantaneous rate is the slope of the curve. Divide each species' rate by its coefficient, and you get one rate for the whole reaction. Reactants take a minus sign, and the units are moles per litre per second. Now go and try the practice problems on this page. All the best!