Use demensional analysis to convert 4.68 grams of boron to cubic centimeters of boron. The density of boron is 2.34 grams per centimeters cubed
(4.68 g)x (1 cm^3 / 2.34 g) = cubic cm of born. The unit of grams is cancelled.
To convert grams of boron to cubic centimeters of boron using dimensional analysis, we can use the given density of boron (2.34 grams per cubic centimeters) as a conversion factor. Here's how to do it step by step:
Step 1: Identify the given and the desired quantities:
Given: 4.68 grams of boron
Desired: cubic centimeters of boron
Step 2: Write down the conversion factor:
Density of boron: 2.34 grams / 1 cubic centimeter
Step 3: Set up the conversion factor as a ratio:
(2.34 grams / 1 cubic centimeter)
Step 4: Choose the appropriate form of the conversion factor to cancel out the given unit and leave the desired unit:
In this case, we want to cancel out the grams of boron to be left with cubic centimeters of boron. To do this, we need to place the conversion factor with grams in the denominator and cubic centimeters in the numerator:
(2.34 grams / 1 cubic centimeter)
Step 5: Multiply the given value by the conversion factor to get the desired quantity:
4.68 grams * (2.34 grams / 1 cubic centimeter)
Step 6: Cancel out the units:
The grams unit cancels out, leaving us with the desired unit of cubic centimeters:
4.68 * (2.34 / 1) cubic centimeters
Step 7: Perform the calculation:
4.68 * 2.34 = 10.9632 cubic centimeters
Step 8: Round the answer to an appropriate number of significant figures:
Since the given quantity has three significant figures, we should round the answer to three significant figures as well:
10.9632 rounded to three significant figures is 10.9 cubic centimeters.
Therefore, 4.68 grams of boron is equivalent to 10.9 cubic centimeters of boron.