Final answer:
The specific heats of metals (Cr, Fe, and Mn) are compared with their atomic weights. A plot is made to show the relationship and reveal any trends. The slope of the best fit line represents how the specific heat capacity changes with atomic weight.
Step-by-step explanation:
The specific heat (c) of a substance is the amount of heat energy required to raise the temperature of one gram of the substance by one degree Celsius. To compare the specific heats of metals (Cr, Fe, and Mn) with their atomic weights, we need to calculate their molar heat capacities first. The molar heat capacity (C) is obtained by multiplying the molar mass (M) of the metal by its specific heat capacity (c). Once we have the molar heat capacities, we can plot them against the atomic weights of the metals.
A trend in the specific heats of the metals may be observed by examining the slopes of the best fit line in the plot. Generally, heavier atoms have lower specific heat capacities compared to lighter atoms. The slope of the best fit line represents the rate at which the specific heat capacity changes with the atomic weight.
For example, let's say we calculate the molar heat capacities of Cr, Fe, and Mn to be 24 J/K, 26 J/K, and 30 J/K, respectively. The atomic weights of Cr, Fe, and Mn are 52 g/mol, 56 g/mol, and 54 g/mol, respectively. When we plot the molar heat capacities against the atomic weights, we may observe that the slope of the best fit line is negative, indicating a decreasing trend of specific heat capacity with increasing atomic weight.