Determining the Densities of Liquids and Solids

Experiment 1 Lab Report Determining the Densities of Liquids and Solids OBJECTIVE: The objective of Experiment 1 was to find the density of an unknown liquid and an unknown solid. DISCUSSION: Density is a standard physical property of a liquid or solid. The density of a subject is expressed as a ratio of the subject’s mass to its’ volume in the following formula: Density = Mass ÷ Volume. At any specified temperature and pressure the density of a sample is constant. Given the specific density of water at various temperatures and solving the density formula for volume we can accurately determine the volume of our container. The mass of the unknown samples are accurately obtained by weighing and using the measuring by difference method. After obtaining the mass and volume of the unknown sample we can calculate the density of that unknown liquid or solid. By design, Experiment 1 provides the data necessary to calculate the density of the unknown liquid and solid. EXPERIMENTAL PROCEDURE: See attached pages. DATA: The data collected and calculated that was used to determine the volume of the pycnometer used throughout the experiment is represented in Table 1: Table 1 Mass of empty stoppered flask Mass of stoppered flask and water Mass of water (calculated) Temperature of water Density of water* Trial 1 63.517g 122.194g 58.677g 20.9℃ 0.9980 g/mL Trial 2 63.515g 122.20g 58.692g 21.4℃ 0.9979 g/mL *Density of water based on temperature The data collected and calculated that was used to determine the density of unknown liquid ‘B’ is represented in Table 2: Table 2 Mass of stoppered flask and liquid B Mass of liquid (calculated) Volume of liquid B (from Table1 calculation) Trial 1 111.590g 48.073g 58.79mL Trial 2 111.581g 48.066g 58.82mL The data collected and calculated that was used to determine the density of unknown metal cylinder is represented in Table 3: Table 3 Mass of stoppered flask and metal Mass of stoppered flask, metal, and water Mass of metal (calculated) Mass of water (calculated) Volume of water (calculated) Volume of metal (calculated) Trial 1 80.682g 133.025g 17.165g 52.343g 52.45mL 6.34mL Trial 2 80.680g 133.084g 17.165g 52.404g 52.51mL 6.31mL For original sheets of data collected see attached pages. CALCULATIONS: To determine the volume of the pycnometer used throughout Experiment 1 the mass of the water used to fill the flask had to be determined. In each trial, mass of the stoppered flask filled with water minus mass of the empty stoppered flask equals mass of the water. In Trial 1 – 122.194g - 63.517g = 58.677g In Trial 1 mass of water in pycnometer is 58.677g. In Trial 2 – 122.207g - 63.515g = 58.692g. In Trial 2 mass of water in pycnometer is 58.692g. The temperature of the water during each trial was used to look-up the density of the water on the internet. Having determined the density and the mass of the water, the volume of the water in the pycnometer was calculated using the following formula – Volume = Mass ÷ Density. In Trial 1 – 58.677g ÷ 0.9980g/mL = 58.79mL In Trial 1 volume of pycnometer is 58.79mL In Trial 2 – 58.692g ÷ 0.9979g/mL = 58.82mL In Trial 2 volume of pycnometer is 58.82mL Having determined the volume of the pycnometer, in order to determine the density of unknown liquid B it is necessary to determine mass of liquid B. Mass of the stoppered flask filled with liquid B minus mass of the empty stoppered flask equals mass of liquid B. In Trial 1 – 111.590g – 63.517g = 48.073g In Trial 1 mass of liquid B is 48.073g. In Trial 2 – 111.581g – 63.515g = 48.066g In Trial 2 mass of liquid B is 48.066g. With a known mass and volume of liquid B the density of liquid B is calculated using the following formula – Density = Mass ÷ Volume. In Trial 1 – 48.073g ÷ 58.79mL = .8177g/mL In Trial 1 density of liquid B is .8177g/mL In Trial 2 – 48.066g ÷ 58.82mL = .8172g/mL In Trial 2 density of liquid B is .8172g/mL To calculate the density of the unknown metal cylinder, first we must determine the mass and volume of the metal cylinder. The mass of the metal cylinder can be determined by subtracting the mass of the empty stoppered flask from the mass of the stoppered flask with the metal cylinder. In Trial 1 – 80.682g – 63.517g = 17.165g In Trial 1 mass of metal cylinder is 17.165g. In Trial 2 – 80.680g – 63.515g = 17.165g In Trial 2 mass of metal cylinder is 17.165g. The volume of the metal cylinder can be determined by calculating the volume of water necessary to fill the flask with the metal cylinder in it and subtracting that amount from the total volume of the flask. Given that Volume = Mass ÷ Density, the volume of water is calculated using the density and mass. To determine the mass of water needed to fill the flask with the metal cylinder, the method measuring by difference is used. Mass of stoppered flask, metal and water minus mass of stoppered flask and metal equals mass of water. In Trial 1 – 133.025g – 80.682g = 52.343g In Trial 1 mass of water is 52.343g. In Trial 2 – 133.084g – 80.680g = 52.404g In Trial 2 mass of water is 52.404g. Given the density of the water (previously determined) and the mass of the water we can calculate the volume of water that was needed to fill the flask with the metal cylinder. Using the formula – Volume = Mass ÷ Density. In Trial 1 – 52.343g ÷ 0.9980g/mL = 52.45mL In Trial 1 volume of water is 52.45mL In Trial 2 – 52.404g ÷ 0.9979g/mL = 52.51mL In Trial 2 volume of water is 52.51mL Using the measuring by difference method, subtracting that calculated volume of water from the total volume of the flask the difference is the volume of the metal cylinder. In Trial 1 – 58.79mL – 52.45mL = 6.34mL In Trial 1 volume of metal cylinder is 6.34mL In Trial 2 – 58.82mL – 52.51mL = 6.31mL In Trial 2 volume of metal cylinder is 6.31mL. Knowing the mass and volume of the metal cylinder, the density of the metal cylinder is calculated using the following formula – Density = Mass ÷ Volume. In Trial 1 – 17.165g ÷ 6.34mL = 2.71g/mL In Trial 1 density of metal cylinder is 2.71g/mL. In Trial 2 – 17.165g ÷ 6.31mL = 2.72g/mL In Trial 2 density of metal cylinder is 2.72g/mL. CONCLUSION: The density of unknown liquid B is determined to be ≈ .8174g/mL (based on the two trials); and the density of the unknown metal cylinder is determined to be ≈ 2.72g/mL (based on the two trials). The significant figures expressed in the final calculation of the density of unknown liquid B is limited to four based on the four significant figures expressed in the density of water. The significant figures expressed in the final calculation of the density of the unknown solid is limited to three based on the three significant figures expressed in the volume of the unknown solid which required rounding to the hundredths place. As there were fewer steps needed for calculating the density of the unknown liquid versus the steps necessary for determining the density of the unknown solid, there is greater confidence in the determined density of unknown liquid B; as we introduce more steps there is more opportunity for error. In spite of the multiple steps used in calculating the densities of the unknown solid and liquid, the determined densities can be presumed reasonably accurate with an insignificant degree of error.