To tackle this problem, we need to break it down into three parts: finding the specific heat, determining the number of moles, and calculating the molar heat capacity of the substance. Let’s go through each step methodically.
Finding the Specific Heat
The specific heat capacity (c) can be calculated using the formula:
q = mcΔT
Where:
- q = heat added (in joules)
- m = mass of the substance (in grams)
- c = specific heat capacity (in J/g°C)
- ΔT = change in temperature (in °C)
From the problem, we know:
- q = 320 J
- m = 37.1 g
- Initial temperature = 26.1°C
- Final temperature = 42.0°C
First, we calculate the change in temperature (ΔT):
ΔT = Final temperature - Initial temperature
ΔT = 42.0°C - 26.1°C = 15.9°C
Now, we can rearrange the formula to solve for specific heat (c):
c = q / (mΔT)
Plugging in the values:
c = 320 J / (37.1 g * 15.9°C)
c = 320 J / 589.49 g°C ≈ 0.543 J/g°C
Calculating the Number of Moles
Next, we need to find the number of moles (n) of the substance present in the sample. The formula for calculating moles is:
n = m / M
Where:
- n = number of moles
- m = mass of the substance (in grams)
- M = molar mass (in g/mol)
Given that the molar mass (M) is 51.4 g/mol, we can substitute the values:
n = 37.1 g / 51.4 g/mol
n ≈ 0.722 moles
Determining the Molar Heat Capacity
The molar heat capacity (C) can be calculated using the specific heat capacity and the molar mass:
C = c * M
Substituting the values we found:
C = 0.543 J/g°C * 51.4 g/mol
C ≈ 27.9 J/mol°C
Summary of Results
To summarize:
- Specific heat of the substance: 0.543 J/g°C
- Number of moles present: 0.722 moles
- Molar heat capacity: 27.9 J/mol°C
This structured approach allows us to systematically solve the problem while ensuring clarity and understanding of the underlying concepts. If you have any further questions or need clarification on any of the steps, feel free to ask!
