QuestionCalculate the mass in pounds of 1.0 gallons of mercury given its density is $13.6 \mathrm{~g} / \mathrm{cm}^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The density of mercury is $13.6 \mathrm{~g} / \mathrm{cm}^{3}$ . We need to find the mass in pounds of1.0 gallons of mercury3. The conversion factors are $1 \mathrm{lb}=453.6 \mathrm{~g}$ and $1 \mathrm{gal}=3.785 \mathrm{~}$

STEP 2

First, we need to convert the volume from gallons to liters.
$Volume\, in\, liters = Volume\, in\, gallons \\times Conversion\, factor$

STEP 3

Now, plug in the given values for the volume in gallons and the conversion factor to calculate the volume in liters.
$Volume\, in\, liters =1.0\, gal \\times3.785\, L/gal$

STEP 4

Calculate the volume in liters.
$Volume\, in\, liters =1.0\, gal \\times3.785\, L/gal =3.785\, L$

STEP 5

Next, we need to convert the volume from liters to cubic centimeters. We know that $1\, L =1000\, cm^{3}$ .
$Volume\, in\, cm^{3} = Volume\, in\, liters \\times Conversion\, factor$

STEP 6

Now, plug in the given values for the volume in liters and the conversion factor to calculate the volume in cubic centimeters.
$Volume\, in\, cm^{3} =3.785\, L \\times1000\, cm^{3}/$

STEP 7

Calculate the volume in cubic centimeters.
$Volume\, in\, cm^{3} =3.785\, L \\times1000\, cm^{3}/ =3785\, cm^{3}$

STEP 8

Now we can calculate the mass in grams using the density of mercury.
$Mass\, in\, grams = Volume\, in\, cm^{3} \\times Density$

STEP 9

Now, plug in the given values for the volume in cubic centimeters and the density to calculate the mass in grams.
$Mass\, in\, grams =3785\, cm^{3} \\times13.6\, g/cm^{3}$

STEP 10

Calculate the mass in grams.
$Mass\, in\, grams =3785\, cm^{3} \\times13.6\, g/cm^{3} =51516\, g$

STEP 11

Finally, we need to convert the mass from grams to pounds.
$Mass\, in\, pounds = Mass\, in\, grams \\times Conversion\, factor$

STEP 12

Now, plug in the given values for the mass in grams and the conversion factor to calculate the mass in pounds.
$Mass\, in\, pounds =51516\, g \\times\, lb/453.6\, g$

STEP 13

Calculate the mass in pounds.
$Mass\, in\, pounds =51516\, g \\times\, lb/453.6\, g =113.6\, lb$ The mass of.0 gallons of mercury is approximately113.6 pounds.

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