Math

QuestionFind the volume (in L) of 2.05×103 g2.05 \times 10^{3} \mathrm{~g} of lithium, given its density is 0.53 g/cm30.53 \mathrm{~g} / \mathrm{cm}^{3}.

Studdy Solution

STEP 1

Assumptions1. The density of Lithium is 0.53g/cm30.53 \, \mathrm{g/cm^3} . The mass of Lithium is .05×103g.05 \times10^{3} \, \mathrm{g}
3. We are asked to find the volume in liters (), where 1cm3=1×1031 \, \mathrm{cm^3} =1 \times10^{-3} \, \mathrm{}

STEP 2

We can find the volume of Lithium using the formula for density, which is mass divided by volume. Rearranging this formula to solve for volume gives usVolume=MassDensityVolume = \frac{Mass}{Density}

STEP 3

Now, plug in the given values for the mass and density to calculate the volume.
Volume=2.05×103g0.53g/cm3Volume = \frac{2.05 \times10^{3} \, \mathrm{g}}{0.53 \, \mathrm{g/cm^3}}

STEP 4

Calculate the volume in cm3\mathrm{cm^3}.
Volume=2.05×103g0.53g/cm3=3867.92cm3Volume = \frac{2.05 \times10^{3} \, \mathrm{g}}{0.53 \, \mathrm{g/cm^3}} =3867.92 \, \mathrm{cm^3}

STEP 5

Now, we need to convert the volume from cm3\mathrm{cm^3} to liters (). We know that 1cm3=1×1031 \, \mathrm{cm^3} =1 \times10^{-3} \, \mathrm{}, so we can use this conversion factor.
Volume=3867.92cm3×1×103/cm3Volume =3867.92 \, \mathrm{cm^3} \times1 \times10^{-3} \, \mathrm{/cm^3}

STEP 6

Calculate the volume in liters.
Volume=386.92cm3×1×103/cm3=3.87Volume =386.92 \, \mathrm{cm^3} \times1 \times10^{-3} \, \mathrm{/cm^3} =3.87 \, \mathrm{}The volume of 2.05×103g2.05 \times10^{3} \, \mathrm{g} of lithium is3.87 liters.

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