A piece of metal alloy (a solution of metals) is made of gold and silver. It is 20% by mass silver. An irregularly shaped piece of this alloy contains 0.356 lb of gold. When the alloy is added to a graduated cylinder that contains 31.55 mL of alcohol, the level in the cylinder rises to 48.77 mL. If alcohol has a density of 0.890 g/cm³, what is the density of the alloy?
convert the lbs of gold to grams. That represents eighty percent of the mass of the alloy sample, so the mass of the sample is massgold/.8
you know the volume of the sample(differences in the volumes of alcohol when submerged).
density alloy= massalloy/volume
Notice the density of the alcohol is given. That is a red herring.
To find the density of the alloy, we need to determine the mass and volume of the alloy.
First, let's find the mass of the alloy. We are given that the piece of alloy contains 0.356 lb of gold. Since the alloy is 20% silver, the remaining 80% must be gold. Therefore, the total mass of the alloy can be calculated as follows:
Total mass of the alloy = mass of gold / percentage of gold in the alloy
Total mass of the alloy = 0.356 lb / 0.8
Total mass of the alloy = 0.445 lb
Next, let's find the volume of the alloy. We are given that the addition of the alloy to the graduated cylinder caused the level to rise from 31.55 mL to 48.77 mL. Therefore, the volume of the alloy is:
Volume of the alloy = 48.77 mL - 31.55 mL
Volume of the alloy = 17.22 mL
However, the density of alcohol is given in grams per cubic centimeter (g/cm³), while the volume of the alloy is given in milliliters (mL). To perform the calculation, we need to convert the volume from milliliters to cubic centimeters:
Volume of the alloy = 17.22 mL * (1 cm³ / 1 mL)
Volume of the alloy = 17.22 cm³
Now we can calculate the density of the alloy:
Density of the alloy = Total mass of the alloy / Volume of the alloy
Density of the alloy = 0.445 lb / 17.22 cm³
To convert pounds to grams, we need to know the conversion factor. The conversion factor is:
1 lb = 453.592 g
Using this conversion factor, we can convert the mass of the alloy from pounds to grams:
Total mass of the alloy = 0.445 lb * 453.592 g/lb
Total mass of the alloy = 201.012 g
Finally, we can calculate the density of the alloy:
Density of the alloy = 201.012 g / 17.22 cm³
Density of the alloy ≈ 11.65 g/cm³
Therefore, the density of the alloy is approximately 11.65 g/cm³.