# The data below were collected for the following reaction at a certain temperature: #X_2Y→2X+Y# (Data found as picture in answer box). What is the concentration of #X# after 12 hours?

##### 2 Answers

#### Explanation:

If you plot a concentration time graph you get an exponential curve like this:

This suggest a first order reaction. I plotted the graph in Excel and estimated the half-life. This is the time taken for the concentration to fall by one half of its initial value.

In this case I estimated the time taken for the concentration to fall from 0.1M to 0.05M. You need to extrapolate the graph to get this.

This gives

So we can see that 12mins = 2 half-lifes

After 1 half life the concentration is 0.05M

So after 2 half-lifes

So in 1L of solution no. moles XY used up = 0.1 - 0.025 = 0.075

Since 2 moles of X form from 1 mole XY the no. moles X formed =0.075 x 2 = 0.15.

So

The concentration of **0.134 M**.

#### Explanation:

The values given to you are

In order to be able to determine what the concentration of **12 hours**, you need to first determine two things

*the order of the reaction**the rate constant*

In order to determine the order of the reaction, you need to plot three graphs

#[X_2Y]# *versus time*, which looks like this

https://plot.ly/~stefan_zdre/3/col2/?share_key=vyrVdbciO8gLbNV6mmucNZ

#ln([X_2Y])# *versus time*, which looks like this

https://plot.ly/~stefan_zdre/17/col2/?share_key=gnsvMoGLJ2NDpZF0dN2B3p

#1/([X_2Y])# *versus time*, which looks like this

https://plot.ly/~stefan_zdre/7/col2/?share_key=M7By0sY6Wvq0W59uTv8Tv6

Now, the graph that fits a **straight line** will determine the reaction's *rate order*. As you can see, the third graph fits this patter, which means that the reaction will be **second-order**.

The integrated rate law for a second-order reaction looks like this

*rate constant* for the given reaction.

In order to determine the value of

To make the calculations easier, I'll pick the first and second values. So, the concentration of **0.100 M** and, after *1 hour*, drops to **0.0856 M**. This means that you have

Use the same equation to determine what the concentration of

Therefore,

To get the concentration fo

You know that *every* **1 mole** of **moles** of *that reacted* is

This is equivalent to

The number of moles of

For your 1-L sample, this is equivalent to a molarity of