Sulfur (3.26 g) is burned in a constant volume calorimeter with excess O2(g). The temperature increases from 21.25°C to 28.22°C. The bomb has a heat capacity of 923 J/K, and the calorimeter contains 815 g of water. Calculate ΔU per mole of SO2 formed, for the following reaction.
S8(s)+ 8 O2(g) 8 SO2(g)
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To calculate the change in internal energy (ΔU) per mole of SO2 formed, we need to determine the heat released or absorbed during the reaction.
First, let's calculate the heat released or absorbed during the reaction using the equation:
q = C × ΔT
where q is the heat released or absorbed, C is the heat capacity of the bomb calorimeter, and ΔT is the change in temperature.
Since the heat capacity is given as 923 J/K, and the change in temperature is ΔT = 28.22°C - 21.25°C = 6.97°C, we need to convert ΔT to Kelvin by adding 273.15:
ΔT = 6.97°C + 273.15 = 280.12 K
Now, calculate q using the equation:
q = 923 J/K × 280.12 K = 258,077.76 J
Next, we need to calculate the moles of SO2 formed. From the balanced equation, we can see that for every mole of S8, 8 moles of SO2 are formed. Therefore, we need to determine the number of moles of S8.
The molar mass of S8 is 256.52 g/mol (8 sulfur atoms in a S8 molecule, each having a molar mass of 32.07 g/mol).
Given that the mass of sulfur burned is 3.26 g:
moles of S8 = mass of sulfur burned / molar mass of S8
= 3.26 g / 256.52 g/mol
= 0.0127 mol
Now, we can calculate the heat ΔU per mole of SO2 formed:
ΔU = q / (moles of S8 × stoichiometric coefficient of SO2)
= 258,077.76 J / (0.0127 mol × 8)
≈ 25,543.47 J/mol
Therefore, the change in internal energy per mole of SO2 formed is approximately 25,543.47 J/mol.