Units of Volume For lunch, Anna and Bill had 12-ounce (oz) cans of soda. What is the volume of a 12.0-oz can of soda in units of milliliters? What is its volume in units of liters?

Question

Units of Volume

For lunch, Anna and Bill had 12-ounce (oz) cans of soda. What is the volume of a 12.0-oz can of soda in units of milliliters? What is its volume in units of liters?

Accepted Answer

To solve this problem using the dimensional-analysis approach (see Math Toolbox 1.3), we determine if there is a relationship between fluid ounces and milliliters:

[latex]\fbox{Volume in ounces}\overset{؟}{\longrightarrow } \fbox{Volume in milliliters}[/latex]

To convert l uid ounces to milliliters we use the following relationship from Table 1.5: 1 oz = 29.57 mL.

[latex]\fbox{Volume in ounces}\overset{1 oz = 29.57 mL}{\longrightarrow } \fbox{Volume in milliliters}[/latex]

We use the equivalence to set up possible conversion ratios:

[latex]\frac{29.57 ml}{1 oz} and \frac{1 oz}{29.57 ml}[/latex]

To convert ounces to milliliters, we can multiply 12.0 oz by the ratio (conversion factor) that will allow like units to cancel:

[latex]Volume in milliliters = 12.0 \cancel{oz} imes \frac{29.57 ml}{1 \cancel{oz}}=355 ml[/latex]

The answer is reported to three significant figures, because the quantity we’re given (12.0 oz) has three significant figures. Consult Math Toolbox 1.2 for details.
The second part of this problem asks you to convert milliliters to liters:

[latex]\fbox{Volume in milliliters}\overset{?}{\longrightarrow } \fbox{Volume in liters}[/latex]

To convert volume in milliliters to volume in liters, we use the following relationship from Table 1.4: 1 mL = 10^–3 L or 1000 mL = 1 L.

[latex]\fbox{Volume in milliliters}\overset{1000 mL = 1 L}{\longrightarrow } \fbox{Volume in liters}[/latex]

This is a unit conversion similar to the conversion we just did for mass. The ratios for converting between milliliters and liters are

[latex]\frac{1 L}{1000 mL} and \frac{1000 mL}{1 L}[/latex]

To convert from milliliters to liters, we can multiply 355 mL by the conversion factor that allows like units to cancel:

[latex]Volume in L = 355 \cancel{mL} imes \frac{1 L}{1000 \cancel{mL}} = 0.355 L[/latex]

Without a single conversion from ounces to liters, the problem we just solved involves multiple steps:

[latex]\fbox{Volume in ounces}\overset{1 oz = 29.57 mL}{\longrightarrow } \fbox{Volume in milliliters}\overset{1000 mL = 1 L}{\longrightarrow } \fbox{Volume in liters}[/latex]

The sequence of steps can be summarized as:

[latex]Volume in liters = 12.0 \cancel{oz} imes \frac{29.57 \cancel{ml}}{1 \cancel{oz}} imes \frac{1 L}{1000 \cancel{mL}}= 0.355 L[/latex]

Question 1.6: Units of Volume For lunch, Anna and Bill had 12-ounce (oz) c...

Related Answered Questions

Density, Volume, and Mass What is the volume of 100.0 g of copper? The density of copper is 8.9 g/cm^3. ...

Verified Answer:

Units of Mass Anna and Bill notice that there are 50.0 mg of sodium in the soda they bought to go with their lunch. How many grams of sodium are present in the can of soda? How many pounds? ...

Verified Answer:

Rounding Numbers Round each of the following numbers to three significant figures: (a) 3245 (b) 12.263 (c) 0.001035 (d) 312,486 (e) 312,586 ...

Verified Answer:

Signiﬁcant Figures in Addition and Subtraction Express the answers to the following operations with the proper number of significant figures: (a) 24 + 1.001 (b) 24 + 1.001 + 0.0003 (c) 428 – 0.01 (d) 14.03 – 13.312 ...

Verified Answer:

Verified Answer:

Units of Temperature The melting point of copper is 1083°C. Above what temperature, in kelvins and degrees Fahrenheit, is copper a liquid? ...

Verified Answer:

Number of Signiﬁcant Figures Determine the number of significant figures in the following: (a) 0.060520 (b) 5020.01 ...

Verified Answer:

Verified Answer:

Forms of Energy Identify examples of potential and kinetic energy in this picture. ...

Verified Answer:

Molecular Motion and Kinetic Energy Which of these two samples of argon gas has more kinetic energy? ...

Verified Answer: