Question 1.37 - Chemistry: Molecular Nature Of Matter And Change

Question

(a) How many cubic meters of milk are in 1 qt (946.4ml)?

(b) How many liters of milk are in 835gal (1gal = 4qt) ?

Step-by-Step Solution

Answer

Answer

$$\begin{gathered} \left(\mathrm{a}\right) \mathrm{The} \mathrm{volume} \mathrm{of} \mathrm{milk} \mathrm{in} 1 \mathrm{qt} \mathrm{is} 9\times 10-4{\mathrm{m}}^3 . \\ \left(\mathrm{b}\right) \mathrm{The} \mathrm{volume} \mathrm{of} \mathrm{milk} \mathrm{in} 835 \mathrm{gal} \mathrm{is} 3.16\times {10}^3\mathrm{L} . \end{gathered}$$

Convert the volume of milk from quarts to cubic meters

The volume of milk can be expressed in the non-SI units of quarts. One quart equals 946.4 mL. Hence, the unit conversion factor for converting quarts to milliliters can be written below:

$\frac{946.4ml}{1qt}$

 

There is a relationship between milliliters and liters, as shown below:

 1L = 10³ml

The ratio of milliliters to liters is written as follows:

$\frac{1L}{{10}^{3}ml}$

The unit conversion equation for converting liters into meters is shown as follows:

 1L = 10^-3m³ 

 

The conversion factor needed to convert liters to meters is shown below:

$\frac{{10}^{-3}{m}^3}{1L}$

Use the above three conversion factors to convert the given volume from quarts to cubic meters as shown below:

$$\begin{gathered} 1qt \times \frac{946.4ml}{1qt} \times \frac{1L}{{10}^{3}ml} \times \frac{{10}^{-3}{m}^3}{1L} =9.464\times {10}^{-4}{m}^3 = 9\times {10}^{-4}{m}^3 \\ \mathrm{Hence}, \mathrm{the} \mathrm{volume} \mathrm{of} \mathrm{milk} \mathrm{in} 1 \mathrm{qt} \mathrm{is} 9\times {10}^{-4}{\mathrm{m}}^3 . \end{gathered}$$

Convert the volume of milk from gallons to liters.

The unit conversion ratio for converting from gallon to quarts is written down by the following equation 1gal = 4qt.

$\frac{4 \mathrm{qt}}{1 \mathrm{gal}}$

The unit analysis setup for this volume conversion is shown below:

$835gal \times \frac{4qt}{1gal} \times \frac{946.4ml}{1qt} \times \frac{1L}{{10}^{3}ml} = 3.16\times {10}^{3}L$

Hence, the volume of milk in 835 gal is found to be $3.16\times {10}^3 L$ .