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4 Steps to Solving Dimensional Analysis Questions

Most students find dimensional analysis problems to be especially intimidating. Often, these problems can be greatly simplified by applying a stepwise approach. If you find dimensional analysis to be difficult, follow the approach in this article. Practice the approach with easy questions first and when when you feel comfortable move to more challenging questions.

1. === Read actively ===

As you read the question, write or underline important information such as volumes, concentrations or number of moles. Then, paraphrase the question to “I am given x and I need to find Y”. For example, if the question reads: How many chloride ions are found in 5g of Magnesium Chloride? You could paraphrase the question to “I am given grams of magnesium chloride, and I am looking for the number of chloride ions”.

2. === Formulate a plan ===

Now, start with what you are given and ask yourself what steps you should take to get to the answer. Next, ask yourself if additional information is needed in order to solve the problem. Additional information may include molar masses, balanced chemical equation(s), conversion factors, or formula(s). Write down the needed equations and calculate your molar masses now.

For example, the question from the previous section requires several steps. First, grams of magnesium chloride must be converted to moles of magnesium chloride. Then, moles of magnesium chloride need to be converted to moles of chloride ions. Finally, moles of chloride ions must be converted to number of ions. Therefore, the question requires a molecular formula for magnesium chloride, the molar mass of magnesium chloride, and Avogadro’s number.

3. === Set up and solve the problem ===

Next, execute your plan. Begin with what you are given, then write the conversion factors and their units. Check that the units cancel out and the unit of the answer remains (e.g., in the problem above, the only unit to remain is molecules of chloride ions). Type the numbers into your calculator and write down the answer along with the unit (e.g., 10*10^20 molecules chloride ions).

4. === Double-check yourself ===

Finally, ask yourself if your answer makes physical sense. For example, if you are asked to calculate number of molecules in a certain number of grams, you would expect a large answer, in the form of x*10^y since there are many molecules in one gram. Practice this process with different types of questions and it will become a second nature. Good Luck!