Determine the instantaneous rate for the following reaction. Here we have methanol reacting with hydrochloric acid to produce chloromethane plus water as a liquid. We are given the times for the reaction at different points and from this we're also given the change in concentration of hydrochloric acid. Now, since we're given all these times and all these concentrations, remember our times will represent X and our concentrations will represent Y.
From this information we can figure out our instantaneous rate by determining the slope. So here Y2 - Y1X2 - X1. We're going to say that this is our first time given to us, which is 0. So we'll say that this is X1 and if this is X1 then this has to be Y1. Now X2 we can make the last time taken, which would be 247, and if this is X2 then this would be Y2. Now we would take those and plug them in.
So we have 1.01 - 1.90 and these are in concentration, so molarity divided by 247.0 - 0.0 in seconds. When we plug this in we get -3.60 × 10-3 molarities per minute. So this will represent our instantaneous rate for the reaction. Notice here that the sign is negative because we can see that the concentration of our reactant overtime is indeed decreasing as we expect it to be.
So this is the approach we would take when they're giving us a list of points for X&Y. We determine what the slope is from these coordinates, and with that we can relate it to our instantaneous rate.