CH100: Fundamentals for Chemistry 1 of 3 Unit Conversion Process Instructor: Tony Zable In chemistry, converting units from one unit system to another (especially within the Metric system) can appear daunting at first glance. However, with a little guidance, and a lot of practice, you can develop the necessary skill set to master this process. To begin, here is a simple mnemonic to guide you through the unit conversion process: 1. Eliminate 2. Replace 3. Relate All unit conversions, regardless of how complex they appear, involve these 3 simple steps. In the following sections, you will be stepped through the unit conversion process using these 3 words as a guide. Example: How many can 25.2 miles/hour be expressed in m/s? i.e. sm ?? hourmiles 25.2 → Note: It is important to recognize that hour 1miles 25.2hourmiles2.25 = Let’s breakdown the unit conversion process into 2 individual processes, miles to meters and hours to seconds: 1. Eliminate – the unit(s) you begin with must be eliminated in a mathematically consistent manner. If a unit to be eliminated is a numerator unit, it must be divided out: sm ?? miles ???? hour 1miles 25.2= If a unit to be eliminated is a denominator unit, it must be multiplied out: sm ?? ??hour ?? hour 1miles 25.2= 2. Replace – the desired unit(s) you end up with must replace the original unit in a mathematically consistent manner. If a unit to replace is a numerator unit, it must be multiplied in: sm ?? miles ??m ?? hour 1miles 25.2= If a unit to be eliminated is a denominator unit, it must be divided in: sm ?? s ??hour ?? hour 1miles 25.2=CH100: Fundamentals for Chemistry 2 of 3 Unit Conversion Process Instructor: Tony Zable 3. Relate – the units must be related to each other in some mathematical expression. Identify the relationship between the starting and final units: 1 mile = 1609 m 1 hour = 3600 s To take the guess work out of where the values should go, match the value with its corresponding unit: For the distance conversion: sm ?? mile 1m 1609 hour 1miles 25.2= For the time conversion: sm ?? s 3600hour 1 hour 1miles 25.2= Putting both conversions together: sm ?? s 3600hour 1 mile 1m 1609 hour 1miles 25.2= Extending the Process: When the explicit relationship between the units is not known, it is often necessary to link them to a common unit (in the “Relate” phase). For example, when converting from mg to kg it is difficult to find a direct expression that relates these units. However, these units can both be related to grams (g) (by replacing the prefix with its corresponding power of 10). 1 mg = 10-3 g 1 kg = 103 g Therefore we can no relate mg to kg. To do so, divide the top expression by the bottom expression: 6-3-310g 10g 10kg 1mg 1== or 1 mg = 10-6 kg Note: the smaller unit (mg) has a larger value and the larger unit (kg) has a smaller value.CH100: Fundamentals for Chemistry 3 of 3 Unit Conversion Process Instructor: Tony Zable Let’s try one: How is 12.5 mg expressed in kg (i.e. 12.5 mg = ___ kg)? 1. Eliminate: {assign mg units to the denominator of the conversion factor} kg ________mg ????1mg 12.5= 2. Replace: {assign kg units to the numerator of the conversion factor} kg ________mg ??kg ??1mg 12.5= 3. Relate: {assign the corresponding value to its unit, using 1 mg = 10-6 kg} kg 1025.11105.12mg 1kg 101mg 12.556-6−−==xkgx Now, it’s your turn: 0.25 nm = ___ cm? 1. Eliminate: cm ?? ??1nm 0.25= {fill-in the blank with correct unit} 2. Replace: cm ?? 1nm 0.25= {fill-in both blanks with correct units} 3. Relate: a) Write-out the relation between nm & m: b) Write-out the relation between cm & m: c) Divide expression (a) by expression (b): d) Solve this expression for the original unit in (a), in this case 1 nm = _____ cm: e) Now put all of the pieces together {fill-in the blanks with correct values and units then do the math }: _____________ 1nm
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