10 Questions
When converting units, why should we place miles on the bottom in the conversion factor?
Because we are trying to cancel out miles
What is the purpose of using multiple conversion factors in a unit conversion problem?
To ensure that the final answer is in the desired unit
Why do we need to use another conversion factor to convert from feet to a desired unit?
Because feet is not a desired unit
What is the result of multiplying by the conversion factor 1 foot = 12 inches?
Feet is cancelled out and inches is introduced
When converting units, why is it essential to set up the problem correctly?
To avoid calculation errors
What is the common issue people face when converting units?
They are not sure whether to multiply or divide
In the conversion of density of ethanol, what is the purpose of multiplying by 1 kg/1,000 g?
To cancel out grams
When converting milliliters to liters, why do we need to manipulate the conversion factor?
To cancel out milliliters
What is the result of multiplying by the conversion factor 1,000 mL/1 L?
Milliliters is cancelled out and liters is introduced
In the conversion of density of ethanol, what is the final answer?
0.8 kg/L
Study Notes
Dimensional Analysis
- Dimensional analysis is a technique used to solve problems in chemistry and everyday life by converting between different units of measurement.
- It allows us to convert a number from one unit to another unit, helping us to solve problems more efficiently and accurately.
Conversion Factors
- A conversion factor is a relationship in the form of an equality, used to convert between different units of measurement.
- Examples of conversion factors include 7 days/1 week, 60 seconds/1 minute, and 12 inches/1 foot.
- Conversion factors can be written in different ways, but they must be equal to 1.
Solving Problems with Dimensional Analysis
- To solve a problem using dimensional analysis, start with the quantity given, and set up a conversion factor (or multiple conversion factors) to solve the problem.
- Identify the known equalities and choose the correct conversion factor to use.
- Multiply the given quantity by the conversion factor, canceling out unwanted units, and arrive at the desired unit of measurement.
One-Step Problems
- Solve the problem of converting 2.45 hours into minutes using the conversion factor 60 minutes/1 hour or 1 hour/60 minutes.
- Choose the correct conversion factor to get the desired unit of measurement.
Multi-Step Problems
- Convert 2.3 miles into centimeters using multiple conversion factors: 1 mile = 5,280 feet, 1 foot = 12 inches, and 1 inch = 2.54 centimeters.
- Set up the problem by listing the conversion factors and using them to cancel out unwanted units, arriving at the desired unit of measurement.
Tips and Tricks
- Always start with the quantity given and work from there.
- Choose the correct conversion factor to cancel out unwanted units and arrive at the desired unit of measurement.
- The order in which you multiply conversion factors does not matter, as long as you cancel out the correct units.
- Dimensional analysis can be used to solve a wide range of problems, from everyday applications to complex chemistry problems.
Learn the technique of dimensional analysis, also known as the factor-label method, to solve problems in chemistry and everyday life. Convert numbers from one unit to another with ease.
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