LAB #3: MEASURING SPECIFIC GRAVITY AND DENSITY. Set-up and Materials for Experiment

1 Set-up and Materials for Experiment

2 OVERVIEW

The mass density of a substance is a measure of the mass that that substance contains in a given volume. Mathematically is written:

ρ =

𝑉

(Mass Density =

)

In the SI system, the units of mass density are g/cm³ or kg/m³. In the English system, weight density (ρw) is commonly used.

ρ

=

𝑉

(Weight Density =

)

In the English system, the unit of weight density is lb/ft³.

The density of a solid may be determined by measuring its mass with balance scales, and dividing by its volume. If the solid is regular, the volume may be found by measurements and calculation. The volume of an irregular solid may be determined by observing the volume of water displaced when it is immersed in water.

A solid object immersed in water displaces an equal volume of water. The object’s weight while in the water because of the displaced water. The apparent weight (wapp) of the object in water is:

w

= w

- w

The buoyant force (FB) on an object immersed in water is equal to the weight of the water it displaces (wwater).

In this lab you’ll measure the mass and volume of an object and calculate its mass density. You will also weigh another object in air and in water to see the difference between actual and apparent weight.

The specific gravity (S.G.) of a substance is a number that states the ratio between the density of a substance and the density of pure water. It is written:

S. G. = 𝜌 𝜌 𝑤𝑎𝑡𝑒𝑟

Either mass density or weight density may be used to find specific gravity, but the units must be identical for the substance and water. If one is calculating the specific gravity using the weight density, the formula would be:

S. G. = 𝜌_𝑤

_{𝑤 (𝑤𝑎𝑡𝑒𝑟)}

In either case, Specific gravity has no units; it is a pure number ratio.

3 OVERVIEW – CONTINUED:

A hydrometer is a device that measures the specific gravity of liquids. You will use a hydrometer in this experiment to measure the specific gravity of some liquids.

The scaled hydrometer is an air-filled tube that is weighted at the bottom and sealed so that it floats upright in liquid. It is placed in water, and the level at which it floats is marked 1.000; any other liquid in which it floats at the same level must have a density equal to water, so its specific gravity is 1.000. If the tube floats higher in an unknown liquid, that liquid is denser than water. If the tube sinks to a lower level, then the liquid is less dense than water. The tube is calibrated in very small increments so that it is very precise, and the specific gravity can be read directly.

The density of the liquid may be determined by measuring the specific gravity with a hydrometer and computing with the equation:

𝜌 = (𝑆. 𝐺. )(𝜌

)

4 OBJECTIVES:

A) Find the density of a solid by measuring its mass and volume.

B) Measure specific gravity of a liquid using a hydrometer C) Compute the density of a liquid, knowing its specific gravity.

EQUIPMENT REQUIRED:

Balance Scales Water

Vernier Calipers Isopropyl Alcohol

0 to 2.5 N Spring Scale 50% RV Antifreeze Hydrometers (two different scales) Hydrometer Cylinder

Small Metal Cylinder Aluminum Cube

Beaker PROCEDURE

I. DENSITY OF A SOLID

1. Sketch the metal cylinder in the space provided in Table 1. Record the type of material in Table 1.

2. Measure the diameter and height of the cylinder, and record the values in the space provided.

3. Using the beam balance, measure and record the mass of the cylinder.

4. Compute the volume of the cylinder in units of cubic centimeters.

Record your answer in Table 1.

5. Calculate the mass density, ρ, in units of grams per cm3, using the equation 𝝆 = ^𝒎_𝑽

Round off the answer according to the rules of accuracy. Record the value in Table 1.

II. MEASURING ACTUAL WEIGHT, APPARENT WEIGHT, AND BUOYANT FORCE.

1. Be sure the spring scale reads “0” with no weight attached. Hang the aluminum cube from the spring scale. Record the reading as the cube’s actual weight in table 2.

2. With the aluminum cube still hanging from the spring scale, immerse the cube in a beaker of water and measure its weight. This is the apparent weight; it whould be less that the actual weight. Record the apparent weight in table 2.

3. Subtract the apparent weight from the actual weight to obtain the weight of water displaced by the cube (this is the buoyant force, FB):

F

= w

- w

Record the buoyant force in table 2.

5 III. SPECIFIC GRAVITY AND DENSITY OF A LIQUID

1. Place a hydrometer (with a 0.65 — 1.0 scale on it) into an empty graduated cylinder and then carefully pour just enough isopropyl alcohol into the cylinder so that the hydrometer begins to float. Read the line on the hydrometer (see the figure below) where the top of the alcohol meets and record this value in Data Table 3 for isopropyl alcohol. Remove the hydrometer, rinse it, and place it back in its box.

2. Calculate the measured mass density using the equation ρ meas = (S.G.)ρwater)

where ρ meas is the measured mass density of the substance, SG is the specific gravity, and ρwater is the mass density of water (1.0 g/ cm³).

Record the measured mass density in Data Table 3.

5. Measure the mass of an empty graduated cylinder on a triple-beam balance. Record its mass at the top of Data Table 3.

6. Pour a small sample of isopropyl alcohol into the graduated cylinder. Read and record its volume in Data Table 3. Measure the combined mass of the alcohol and graduated cylinder on a triple-beam balance. Subtract the mass of the beaker from this value to obtain the mass of the isopropyl alcohol sample. Record the mass of the sample.

7. Calculate the calculated mass density of the sample using the equation:

𝜌 𝑐𝑎𝑙𝑐 =𝑚 𝑉

where ρ calc is the mass density of the substance, m is the mass and V is the volume.

8. Calculate the percent difference (%Δ) between your two mass density values using the equation

%𝛥 = | 𝜌_{𝑐𝑎1𝑐}− 𝜌_{𝑚𝑒𝑎𝑠} |

𝜌_{𝑚𝑒𝑎𝑠} 𝑥 100.0%

The vertical brackets in the numerator indicate that you are to use the absolute value of 𝜌_{𝑐𝑎1𝑐} − 𝜌_{𝑚𝑒𝑎𝑠}.

9. Repeat steps C-2 through C-7 for the 50% anti-freeze mixture. Disregard the range of values given in step C-2. We will do two samples only.

NOTE: For question #1 on the analysis page, compare the two mass density values, rather than the two mass values.

6 OBJECTIVES: SKETCH OF LAB SET-UP:

TABLE 1: DENSITY OF A SOLID OBJECT

Sketch: Dimensions Volume

V (cm³)

Mass m (grams)

Mass Density  (g/cm³)

Material:____________________Text Book Density Value__________

TABLE 2: ACTUAL AND APPARENT WEIGHT OF AN OBJECT Actual Weight of Aluminum

Cube (N)

Apparent Weight of Cube (N) Buoyant Force (weight of water displaced) (N)

TABLE 3: SPECIFIC GRAVITY OF A LIQUID

Mass of Beaker:__________ Mass of Beaker and Sample: 1) _________ 2) _________

Specific Gravity

(Float Reading)

Mass Density

 (g/cm³)

Sample Volume

V (cm³)

Calculated Sample Mass m (grams)

Calculated Sample Density

 (g/cm³)

% Difference

=

100%

x

BestValue

| -

| _{calc meas}

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  

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