Hi! I'm having trouble solving this question, not sure how to go about starting it:
Magnalium is a solid mixture of aluminum metal & magnesium metal. An irregular shaped chunk of a sample of magnalium is weighed twice, once in air (211.5g) and once in vegetable oil (135.3g) by using a spring scale. If the densities of pure aluminum, pure magnesium, & vegetable oil are 2.70g/cm^3, 1.74g/cm^3, and 0.926g/cm^3, respectively, then what is the mass percent of magnesium in the chunk of magnalium? Assume that the density of a mixture of the two metals is a linear function of the mass percent composition.
Thanks.
To solve this question, we can use the concept of density and mass percent composition.
Let's break down the problem and identify the key information given:
1. The weight of the magnalium chunk in air = 211.5g
2. The weight of the magnalium chunk in vegetable oil = 135.3g
3. The densities of pure aluminum, pure magnesium, and vegetable oil are given as 2.70g/cm^3, 1.74g/cm^3, and 0.926g/cm^3, respectively.
Now, let's start solving the problem step by step:
Step 1: Calculate the volume of the magnalium chunk in air using its weight and the density of air.
- The density of air is very close to 0. The weight of the chunk in air gives us its mass.
- Since density = mass/volume, rearrange the formula to isolate the volume: volume = mass/density.
- The volume of the magnalium chunk in air = 211.5g / 0 = 0 cm^3.
Step 2: Calculate the volume of the magnalium chunk in vegetable oil using its weight and the density of vegetable oil.
- The volume of the chunk in vegetable oil = 135.3g / 0.926g/cm^3.
- The volume of the chunk in vegetable oil = 146.3 cm^3.
Step 3: Find the volume of aluminum and magnesium in the magnalium chunk.
- Let's assume the magnalium chunk contains x grams of magnesium, therefore, the remaining (211.5 - x) grams would be aluminum.
- The volume occupied by aluminum = (211.5 - x) g / 2.70 g/cm^3.
- The volume occupied by magnesium = x g / 1.74 g/cm^3.
Step 4: Use the assumption that the density of the mixture is a linear function of the mass percent composition.
- The density of the magnalium chunk = (volume of aluminum x density of aluminum) + (volume of magnesium x density of magnesium).
- The density of the magnalium chunk = ((211.5 - x) / 2.70) + (x / 1.74).
Step 5: Equate the above expression of density with the density of vegetable oil to solve for x.
- ((211.5 - x) / 2.70) + (x / 1.74) = 146.3 / 0.926.
Solve this equation to find the value of x, which represents the mass of magnesium in the magnalium chunk.
Step 6: Calculate the mass percent of magnesium.
- Mass percent of magnesium = (mass of magnesium / total mass of magnalium) x 100.
Plug in the value of x into the above equation to get the mass percent of magnesium in the magnalium chunk.
By following these steps, you will be able to solve the question and find the mass percent of magnesium in the magnalium chunk.
you know mass (same as in air)
find volume from density of oil
densityoil*volume=difference in masses air vs oil.
Now, density=mass/volume
then you have a linear equation
DensityMagnesium*volumetotal*PercentMg + DensityAl*volumetotal*(1-percentMg)=massblock
solve for percentMg, then you have percentAl (percents are in decimal form)