You would like to determine if a set of antique silverware
is pure silver. The mass of a small fork was measured on a
balance and found to be 80.56 g. The volume was found by
dropping the fork into a graduated cylinder initially containing 10.0 mL of water. The volume after the fork was added
was 15.90 mL. Calculate the density of the fork. If the density of pure silver at the same temperature is 10.5 g/cm3, is the fork pure silver?
The answer I got was that the fork is not pure silver, because if it was the water would rise to 17.67 ml. Am I correct?
Yes, you are correct that if the fork were made of pure silver the volume should have been 17.67 mL. I wouldn't have done it that way. I would have calculated the density and compared it with 10.5 g/mL for pure Ag.
density = mass/volume = 80.56/5.90 = 13.65 g/mL which isn't 10.5 g/mL. I should point out that pure silver is almost NEVER used. It is too soft and it usually is alloyed with another metal. I looked in a table of densities and found Au and Am having a density in the 13.5 range. I don't know what the fork is but it isn't pure silver.
No, you are not correct. While your method of comparing the observed volume increase with the expected volume increase for pure silver is interesting, it is not accurate enough for determining the purity of the fork.
To calculate the density of the fork, you need to divide its mass by its volume. In this case, the mass of the fork is 80.56 g and the volume is the difference between the final and initial volumes of water in the graduated cylinder, which is (15.90 mL - 10.0 mL = 5.90 mL).
Density = mass/volume
Density = 80.56 g / 5.90 mL
However, before proceeding further, you need to convert the volume from milliliters (mL) to cubic centimeters (cm^3) since density is typically expressed in g/cm^3.
Volume (in cm^3) = 5.90 mL * (1 cm^3 / 1 mL)
Volume = 5.90 cm^3
Now, you can calculate the density:
Density = 80.56 g / 5.90 cm^3
Density ≈ 13.69 g/cm^3
The density you calculated for the fork (13.69 g/cm^3) is higher than the density of pure silver (10.5 g/cm^3). Thus, based on density alone, it is more likely that the fork contains impurities and is not made of pure silver.
To determine the density of the fork, we need to use the formula: density = mass/volume.
Given:
Mass of fork (m) = 80.56 g
Initial volume of water (V1) = 10.0 mL
Final volume of water with fork (V2) = 15.90 mL
First, let's calculate the volume of the fork:
Volume of fork (Vfork) = V2 - V1
= 15.90 mL - 10.0 mL
= 5.90 mL
Next, we can calculate the density of the fork:
Density of fork = mass/volume
= 80.56 g / 5.90 mL
= 13.66 g/mL
Now, let's compare the density of the fork to the density of pure silver (10.5 g/cm3). Since the density of the fork is 13.66 g/mL, which is greater than the density of pure silver, it suggests that the fork is not made of pure silver.
Therefore, you are correct in concluding that the fork is not pure silver.
To determine if the fork is made of pure silver, we need to calculate its density and compare it to the density of pure silver. Here's how you can calculate the density:
1. Calculate the volume of the fork:
Volume = Final volume - Initial volume
Volume = 15.90 mL - 10.0 mL
Volume = 5.90 mL
2. Convert the volume to cm³:
1 mL = 1 cm³, so 5.90 mL = 5.90 cm³
3. Calculate the density:
Density = Mass / Volume
Density = 80.56 g / 5.90 cm³
Now, let's plug in the values to calculate the density of the fork:
Density = 80.56 g / 5.90 cm³
Density ≈ 13.68 g/cm³
The density of the fork is approximately 13.68 g/cm³.
Next, we compare the density of the fork to the density of pure silver, which is given as 10.5 g/cm³. Since the fork's density is higher than the density of pure silver, we can conclude that the fork is not made of pure silver.
Therefore, your conclusion that the fork is not pure silver is correct. The water displacement observation you mentioned is also consistent with this conclusion.