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QuestionWhat is the new water level in mL after adding 7.25 g of silver to 11.8 mL of water? Use the density of silver: 10.5 g/cm310.5 \mathrm{~g} / \mathrm{cm}^{3}.

Studdy Solution

STEP 1

Assumptions1. The density of pure silver is 10.5 g/cm310.5 \mathrm{~g} / \mathrm{cm}^{3} at 20∘C20^{\circ} \mathrm{C} . The mass of the silver pellets is 7.25 g7.25 \mathrm{~g}
3. The initial volume of the water in the graduated cylinder is 11.8 m11.8 \mathrm{~m}
4. The volume of the silver pellets can be calculated using their density and mass5. The volume of the water will increase by the volume of the silver pellets

STEP 2

We need to find the volume of the silver pellets. We can do this by dividing the mass of the silver by its density.
Volume=MassDensityVolume = \frac{Mass}{Density}

STEP 3

Now, plug in the given values for the mass and density of the silver to calculate the volume.
Volume=7.25 g10.5 g/cm3Volume = \frac{7.25 \mathrm{~g}}{10.5 \mathrm{~g/cm}^{3}}

STEP 4

Calculate the volume of the silver pellets.
Volume=7.25 g10. g/cm3=0.69 cm3Volume = \frac{7.25 \mathrm{~g}}{10. \mathrm{~g/cm}^{3}} =0.69 \mathrm{~cm}^{3}

STEP 5

We need to convert the volume of the silver pellets from cubic centimeters to milliliters because the volume of the water is given in milliliters. We can do this by using the fact that1 cubic centimeter is equal to1 milliliter.
Volume=0.69 cm3=0.69 mVolume =0.69 \mathrm{~cm}^{3} =0.69 \mathrm{~m}

STEP 6

Now that we have the volume of the silver pellets, we can find the final volume of the water in the graduated cylinder. This is the initial volume of the water plus the volume of the silver pellets.
Final volume=Initial volume+Volume of silver pelletsFinal\, volume = Initial\, volume + Volume\, of\, silver\, pellets

STEP 7

Plug in the values for the initial volume of the water and the volume of the silver pellets to calculate the final volume.
Final volume=11. m+0.69 mFinal\, volume =11. \mathrm{~m} +0.69 \mathrm{~m}

STEP 8

Calculate the final volume of the water in the graduated cylinder.
Final volume=11.8 m+0.69 m=12.49 mFinal\, volume =11.8 \mathrm{~m} +0.69 \mathrm{~m} =12.49 \mathrm{~m}The volume level of the water in the cylinder will rise to12.49 mL.

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