Inside width of graduated cylinder:
(± 0.1cm / 2.5cm) * 100 = ± 4%
Balance:
Mass of 25mL graduated cylinder:
(± 0.1g / 50.8g) * 100 = ± 0.197%
Mass of 25mL cylinder with water and metal:
(± 0.01g / 121.85g) * 100 = ± 0.008%
25mL graduated cylinder:
Volume of water and cylinder:
(± 0.1g / 65.1g) * 100 = ± 0.154%
2.) Solid volume of a 100mL graduated cylinder up to 50mL mark is obtained by first finding the volume; (V = πr²h). Pi is 3.1416, and the radius is determined by dividing the diameter of the 100mL graduated cylinder (2.5cm) in half, or 1.25cm. The height of the 50mL mark is 9.5cm. The formula is V = 3.1416 * (2.5cm)² * 9.5cm, or 46.63mL³.
3.) The experimental error looks like this:
(50.00 - 46.63mL³) / (50.00) * 100 = 6.74% error
4.) Mass of water is determined by subtracting the mass of the 25mL cylinder from the measured mass of the 25mL cylinder and water, or: 65.1g - 50.8g = 14.3g
The mass of the water according to the density formula is D = M / V, or 0.997569= m / 16mL, or 15.961g. The experimental error looks like this:
(14.3g - 15.961g) / (14.3g) * 100 = 11.6% error.
5.) The volume of the metal is obtained by subtracting the volume of the water from the combined volume of the water and the metal. 23mL - 16mL = 7mL volume for the metal. The mass of the metal is attained by subtracting the mass of the cylinder and water from the mass of the cylinder, water, and metal. 121.85g - 65.1g = 56.8g. The density of the metal is mass over volume, or 56.8g / 7mL = 8 g/mL.
6.) Metal densities for other groups:
1. V = 21.5mL - 15mL = 7mL
M = 119.5g - 63.2g = 56.3g
D = 56.3g / 7mL = 8 g/mL
2. V = 19.2mL - 12.5mL = 6.7mL
M = 120g - 62.2g = 58g
D = 58g / 6.7mL = 8.7 g/mL
4. V = 18mL - 12.5mL = 6mL
M = 119.2g - 61.9g = 57.3g
D = 57.3g / 6mL = 10 g/mL
5. V = 20.5mL - 14mL = 7mL
M = 121.6g - 63.4g = 58.2g
D = 58.2g / 7mL = 8 g/mL
6. V = 20.5mL - 14mL = 7mL
M = 121.65g - 63.35g = 58.3g
D = 58.3g / 7mL = 8 g/mL
Average Density = 8.54 g/mL
7.) Our density value of out metal (using significant figures) is 8 g/mL. The class average is 8.54 g/mL. This value comes closest to the density of nickel. Our group’s density come closest to that of antimony.
8.) The percent error of our density:
(8.9 - 8) / (8.9) * 100 = 11.25% error
The percent error for the class’ density
(8.9 - 8.54) / (8.9) * 100 = 4.04% error.
The class average density has a much lower percent error than our own group’s.
Extensions:
1.) Marie and Jason were precise with their measurements, but not accurate. Their average density was 2.83g/mL. Their experimental error was such:
(2.4 - 2.83) / (2.4) * 100 = 17.9% error.
Their uncertainty was such:
(±0.01 / 2.83) * 100 = 0.353% uncertainty.
2.) When cutting legs off a table, precision is always better than accuracy. When precise, the same amount from each table leg will be cut, keeping the table even. The accuracy, though, can only be determined if the measurement is already know.
