It takes 100 J to raise the temperature of 14.4 g of ortho-carborane by 8.3 oC. What is the molar heat capacity of ortho-carborane if its molecular formula is C2B10H12 (MW = 144.44)? Give your answer in J/K.mol to 1 d.p Useful Formula...!q = c m ΔTc = q/m*ΔT
Question
It takes 100 J to raise the temperature of 14.4 g of ortho-carborane by 8.3 oC. What is the molar heat capacity of ortho-carborane if its molecular formula is C2B10H12 (MW = 144.44)? Give your answer in J/K.mol to 1 d.p Useful Formula...!q = c m ΔTc = q/m*ΔT
Solution
Sure, let's solve this step by step.
Step 1: Calculate the number of moles of ortho-carborane.
The molar mass of ortho-carborane (C2B10H12) is given as 144.44 g/mol. So, the number of moles (n) can be calculated using the formula:
n = mass / molar mass n = 14.4 g / 144.44 g/mol = 0.1 mol
Step 2: Calculate the heat absorbed (q) using the given formula.
q = c * m * ΔT
We know that q = 100 J, m = 14.4 g, and ΔT = 8.3 °C. We can rearrange the formula to solve for c (specific heat capacity):
c = q / (m * ΔT) c = 100 J / (14.4 g * 8.3 °C) = 0.85 J/g.°C
Step 3: Convert the specific heat capacity (c) to molar heat capacity (C).
C = c * molar mass C = 0.85 J/g.°C * 144.44 g/mol = 122.77 J/mol.°C
So, the molar heat capacity of ortho-carborane is 122.8 J/K.mol (rounded to 1 decimal place).
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