Question

1. in an experiment performed at 20°c, the mass of a dry empty flask is found to be 36.2142g. when the flask is filled with water, the mass is 46.1849g. when a small sample of a metal is added to the dry, empty flask, the mass is 38.1055g. finally, when the flask with the sample of metal is filled with water the measured mass is 47.8161g. use this data together with the density of water at 20°c as 0.99823g/ml to determine the density of the metal. your answer should contain the correct number of significant figures.

Explanation:

Step1: Find mass of water in flask

Mass of water = Mass of flask + water - Mass of empty flask
$m_{water} = 46.1849\,\text{g} - 36.2142\,\text{g} = 9.9707\,\text{g}$

Step2: Find volume of flask (from water)

Volume = $\frac{\text{Mass}}{\text{Density}}$
$V_{flask} = \frac{9.9707\,\text{g}}{0.99823\,\text{g/mL}} \approx 9.9884\,\text{mL}$

Step3: Find mass of metal

Mass of metal = Mass of flask + metal - Mass of empty flask
$m_{metal} = 38.1055\,\text{g} - 36.2142\,\text{g} = 1.8913\,\text{g}$

Step4: Find mass of water with metal in flask

Mass of water (with metal) = Mass of flask + metal + water - Mass of flask + metal
$m_{water\,(with\,metal)} = 47.8161\,\text{g} - 38.1055\,\text{g} = 9.7106\,\text{g}$

Step5: Find volume of water with metal

$V_{water\,(with\,metal)} = \frac{9.7106\,\text{g}}{0.99823\,\text{g/mL}} \approx 9.7278\,\text{mL}$

Step6: Find volume of metal

$V_{metal} = V_{flask} - V_{water\,(with\,metal)}$
$V_{metal} = 9.9884\,\text{mL} - 9.7278\,\text{mL} = 0.2606\,\text{mL}$

Step7: Find density of metal

Density = $\frac{\text{Mass}}{\text{Volume}}$
$
ho_{metal} = \frac{1.8913\,\text{g}}{0.2606\,\text{mL}} \approx 7.258\,\text{g/mL}$ (round to appropriate sig figs)

Answer:

$\boxed{7.26\,\text{g/mL}}$ (or $7.25\,\text{g/mL}$ depending on rounding, but typically 7.26 with given sig figs)