# A simple unit conversion problem that I don't get.

• JerusalemLuver
In summary, the conversation discusses how to calculate the enthalpy change per mole in a problem involving a given volume and molar density of a substance. The given molar density is 1.00 mol dm^-3, which can also be written as 1.00 mole / dm^3. The confusion arises from the use of negative exponents, which can be rewritten as positive exponents. It is then clarified that 1 dm^3 is equal to 1000 cubic centimeters, and that 1 decimeter is equal to 10 centimeters.
JerusalemLuver
The question is a enthalopy problem where the enthalopy has to be caluculated per mole at the end. I understand how to calculate the enthalopy change, but I can't seem to calculate the number of moles in the question to be able to calculate the change in enthalapy per mole. I'm given 50.0 cm^3 of 1.00 mol dm^-3 of a substance. The answer is given so I know it's 0.05 moles but how was that calculated? And also why is it dm^-3 and not dm^3?

I know that a cm is a hundreth of a meter and a dm is 10cm/meter or is it? I'm really confused about my units (especially the cubed parts) so if someone can clarify all this it would be greatly appreciated.

You are given a molar “density” (moles per unit volume) of your substance as well as the volume of the substance used in the reaction.

Your molar density is given as,
1.00 mol dm^-3

Now you asked why it is dm^-3 and not dm^3….maybe it is because of this fact that you did not realize you were given a density.
Remember the ‘rules of exponents’…a negative exponent in the numerator of a fraction can be re-written as a positive exponent in the denominator of a fraction. So if you were to move the dm term to the denominator of the fraction you would get,
1.00 mole / dm^3
And of course dm^3 is a unit of volume equal to 1000 cubic centimeters (10 cm * 10 cm * 10 cm = 1000 cm^3 = 1 dm^3).

So now you know how many moles of your substance are in a given volume, and you also know the volume (50.0 cm^3), so you should be able to calculate the number of moles.

Still a bit confused...

You're right I forgot about the rule of exponents, but I'm still a bit confused about "And of course dm^3 is a unit of volume equal to 1000 cubic centimeters (10 cm * 10 cm * 10 cm = 1000 cm^3 = 1 dm^3)." can anyone simplify this concept any further?
P.S. Is 1dm = 10cm ?

The prefix "deci-" (abbreviated "d" here) means one tenth. Deciliter is 100 mL and decimeter is 10 cm.

## 1. What is a unit conversion problem?

A unit conversion problem involves converting a measurement from one unit to another, typically within the same system of measurement. It can involve converting between units of length, mass, volume, time, or any other measurable quantity.

## 2. Why do we need to know how to do unit conversions?

Unit conversions are necessary for accurate and consistent measurements. Different countries and industries may use different units of measurement, so being able to convert between units allows for effective communication and data analysis.

## 3. How do you solve a unit conversion problem?

To solve a unit conversion problem, you need to know the conversion factor between the two units. Multiply the starting value by the conversion factor to get the equivalent value in the desired unit. It is important to keep track of units and perform any necessary conversions along the way.

## 4. What are some common unit conversion formulas?

Some common unit conversion formulas include: 1 inch = 2.54 centimeters, 1 pound = 0.453592 kilograms, 1 gallon = 3.78541 liters, and 1 minute = 60 seconds. It is important to use the correct conversion factor for the specific units being converted.

## 5. Can you give an example of a unit conversion problem?

Sure, an example of a unit conversion problem would be converting 10 kilometers to miles. The conversion factor between kilometers and miles is 0.621371, so to solve the problem, we would multiply 10 kilometers by 0.621371 to get 6.21371 miles. Therefore, 10 kilometers is equal to 6.21371 miles.

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