Wrksht 2

Density Worksheet Overview

Basic Formulas

  • Volume of a Cylinder:
    V=r2hV = r^2 h

  • Volume of a Cube:
    V=LimesWimesHV = L imes W imes H

  • Conversion Factor:
    454extg=1extlb454 ext{ g} = 1 ext{ lb}

Density Values (g/mL)

  • Nickel (Ni): 8.90

  • Potassium (K): 0.86

  • Zinc (Zn): 7.14

  • Tungsten (W): 19.35

  • Mercury (Hg): 13.59

Example Calculations

1. Density and Specific Gravity of a Block of Wood

  • Given Data:

    • Weight of wood = 47.93 g

    • Height = 5.32 cm

    • Width = 0.0496 m (converted: 4.96 cm)

    • Length = 41.2 mm (converted: 4.12 cm)

  • Volume Calculation:
    V=4.12imes4.96imes5.32=108.72extcm3V = 4.12 imes 4.96 imes 5.32 = 108.72 ext{ cm}^3

  • Density Calculation:
    d=rac47.93extg108.72extcm3=0.441extg/cm3d = rac{47.93 ext{ g}}{108.72 ext{ cm}^3} = 0.441 ext{ g/cm}^3

  • Specific Gravity Calculation:

    • SG = 0.441

2. Density of Water

  • Given Data:

    • Volume = 21.6 mL

    • Weight = 21.49 g

  • Density Calculation:
    d=rac21.49extg21.6extmL=0.995extg/mLd = rac{21.49 ext{ g}}{21.6 ext{ mL}} = 0.995 ext{ g/mL}

3. Density and Specific Gravity of a Rock

  • Given Data:

    • Initial volume = 9.00 mL

    • Final volume = 12.14 mL (after rock addition)

    • Weight of rock = 9.18 g

  • Volume Calculation:
    V=12.14extmL−9.00extmL=3.14extmLV = 12.14 ext{ mL} - 9.00 ext{ mL} = 3.14 ext{ mL}

  • Density Calculation:
    d=rac9.18extg3.14extmL=2.92extg/mLd = rac{9.18 ext{ g}}{3.14 ext{ mL}} = 2.92 ext{ g/mL}

4. Density Using Archimedes' Principle

  • Given Data:

    • Weight in air = 23.463 g

    • Weight in water = 21.374 g

    • Density of water at 25°C = 0.998 g/mL

  • Buoyant Force Calculation:
    BF=23.463extg−21.374extg=2.089extgBF = 23.463 ext{ g} - 21.374 ext{ g} = 2.089 ext{ g}

  • Volume Calculation:
    V=rac2.089extg0.998extg/mL=2.094extmLV = rac{2.089 ext{ g}}{0.998 ext{ g/mL}} = 2.094 ext{ mL}

  • Density Calculation:
    d=rac23.463extg2.094extmL=11.21extg/mLd = rac{23.463 ext{ g}}{2.094 ext{ mL}} = 11.21 ext{ g/mL}

5. Volume and Density of a Cylinder

  • Given Data:

    • Radius = 2.63 cm

    • Height = 1.72 cm

    • Weight = 78.53 g

  • Volume Calculation:
    V=extπimes(2.63)2imes1.72=37.4extcm3V = ext{π} imes (2.63)^2 imes 1.72 = 37.4 ext{ cm}^3

  • Density Calculation:
    d=rac78.53extg37.4extcm3=2.10extg/cm3d = rac{78.53 ext{ g}}{37.4 ext{ cm}^3} = 2.10 ext{ g/cm}^3

  • Specific Gravity Calculation:

    • SG = 2.10

6. Specific Gravity of Isopropyl Alcohol

  • Given Data:

    • Specific gravity = 0.781

  • Density Calculation:
    d=0.781extg/mLd = 0.781 ext{ g/mL}

  • Weight Calculation for 5 L:

    • Convert Volume: 5 L = 5000 mL

    • Mass Calculation:
      m=0.781extg/mLimes5000extmL=3905extg=3.905extkgm = 0.781 ext{ g/mL} imes 5000 ext{ mL} = 3905 ext{ g} = 3.905 ext{ kg}

    • Convert to lbs:
      3.905extkgimesrac2.204621extkg=8.61166extlbs3.905 ext{ kg} imes rac{2.20462}{1 ext{ kg}} = 8.61166 ext{ lbs}

7. Weight of a Nickel Cube

  • Given Data:

    • Side length = 23.00 mm (converted: 2.30 cm)

  • Volume Calculation:
    V=(2.30extcm)3=12.17extcm3V = (2.30 ext{ cm})^3 = 12.17 ext{ cm}^3

  • Mass Calculation:
    M=8.90extg/cm3imes12.17extcm3=108.39extgM = 8.90 ext{ g/cm}^3 imes 12.17 ext{ cm}^3 = 108.39 ext{ g}

8. New Water Level After Adding Tungsten and Zinc

  • Given Data:

    • Piece of tungsten = 10.00 g

    • Piece of zinc = 14.56 g

  • Volume Calculations:

    • Zinc:
      VZn=rac14.56extg7.14extg/mL=2.04extmLV_{Zn} = rac{14.56 ext{ g}}{7.14 ext{ g/mL}} = 2.04 ext{ mL}

    • Tungsten:
      VW=rac10.00extg19.35extg/mL=0.517extmLV_{W} = rac{10.00 ext{ g}}{19.35 ext{ g/mL}} = 0.517 ext{ mL}

  • Total Volume Displacement:
    Vtotal=2.04extmL+0.517extmL=2.557extmLV_{total} = 2.04 ext{ mL} + 0.517 ext{ mL} = 2.557 ext{ mL}

  • New Water Level:
    Vnew=35.0extmL+2.557extmL=37.56extmLV_{new} = 35.0 ext{ mL} + 2.557 ext{ mL} = 37.56 ext{ mL}

9. Volume of a Potassium Piece

  • Given Data:

    • Mass = 3.82 x 10^4 g

  • Volume Calculation:

    • Using density of potassium:
      V=rac3.82imes104extg0.86extg/mL=4.44imes104extmLV = rac{3.82 imes 10^4 ext{ g}}{0.86 ext{ g/mL}} = 4.44 imes 10^4 ext{ mL}

10. Weight of a Beaker of Mercury

  • Given Data:

    • Volume = 4 L (converted: 4000 mL)

  • Mass Calculation:
    M=13.59extg/cm3imes4000extcm3=5.436imes104extgM = 13.59 ext{ g/cm}^3 imes 4000 ext{ cm}^3 = 5.436 imes 10^4 ext{ g}

  • Convert to lbs:
    extlbs=rac5.436imes104extg454extg/lb=119.9165extlbsext{lbs} = rac{5.436 imes 10^4 ext{ g}}{454 ext{ g/lb}} = 119.9165 ext{ lbs}

Final Answers Summary

  1. Density: 0.441 g/mL; Specific Gravity: 0.441

  2. Density: 0.995 g/mL

  3. Density: 2.92 g/mL; Specific Gravity: 2.92

  4. Density: 11.21 g/mL

  5. Volume of Cylinder: 37.4 cm³; Density: 2.10 g/mL; Specific Gravity: 2.10

  6. Density of Isopropyl Alcohol: 0.781 g/mL; Weight: 4000 g; 9 lbs

  7. Weight of Nickel Cube: 108.39 g

  8. New Water Level: 37.56 mL

  9. Volume of Potassium: 4.44 x 10^4 mL

  10. Weight of Mercury Beaker: 5 x 10^4 g; 100 lbs