Solving Dimensional Analysis Problems

Knowing how to solve problems using dimensional analysis is critical in chemistry. We will go through an example below:

Let's say we would like to calculate the number of seconds in 1 year. Before we start, we need to write down the various conversion factors that will be useful in solving this problem.

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

365 days = 1 year

Therefore the equation to work this out will be:

$$\newcommand{\ctext}[1]{\style{font-family:Arial}{\text{#1}}}\begin{align*} &1\ctext{ year}\times \frac{365\ctext{ days}}{1\ctext{ year}}\times\frac{24\ctext{ hours}}{1\ctext{ day}}\times \frac{60\ctext{ min}}{1\ctext{ hour}}\times \frac{60\ctext{ secs}}{1\ctext{ min}}\cr &= 1\times \frac{365}{1}\times \frac{24}{1}\times \frac{60}{1}\times \frac{60\ctext{ secs}}{1}\end{align*}$$

Now that all the units have been cancelled out except seconds, we simply multiply the equation.

$$ 365 \times 24 \times 60 \times 60\ctext{ seconds} = 31,536,000\ctext{ seconds}$$

Therefore, there are 31,536,000 seconds in a year.

There is a video on the next page that demonstrates how to answer a typical dimensional analysis question you may come across in chemistry and also some sample questions.

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