Complete Question:
A hypothetical alloy is composed of 25 wt% of metal A and 75 wt% of metal B. The densities of metal A and metal B are 6.17 g/cm³ and 8.00 g/cm³, respectively. Calculate the overall density of the alloy.
Answer:
The hypothetical alloy composed of 25 wt% metal A and 75 wt% metal B will have a density of 7.25 g/cm³. To calculate the density of the alloy, we need to consider the weighted average of the densities of metal A and metal B based on their respective weight percentages.
Calculating the Density of a Hypothetical Alloy
Given Data:
- Metal A weight percentage: 25%
- Metal B weight percentage: 75%
- Density of metal A: 6.17 g/cm³
- Density of metal B: 8.00 g/cm³
Formula:
Density of Alloy = (Weight Percentage of A * Density of A) + (Weight Percentage of B * Density of B)
Calculations:
Density of Alloy = (0.25 * 6.17 g/cm³) + (0.75 * 8.00 g/cm³)
Density of Alloy = 1.5425 g/cm³ + 6.00 g/cm³
Density of Alloy = 7.5425 g/cm³
Rounding off to the appropriate number of significant figures, the density of the alloy is 7.25 g/cm³.
By using the given data and applying the formula for calculating the density of the alloy based on the weighted average of metal A and metal B, we have determined that the overall density of the hypothetical alloy is 7.25 g/cm³.