a 9.85 g sample of an unknown metal M is burned in the presence of excess oxygen, producing the oxide M2O3 (s) and liberating 57.8kJ of heat at constant pressure. What is the identity of the metal?
4M(s) + 3O2(g) yields 2M2O3(s)
Do you have a table of heats of combustion?
To determine the identity of the metal, we need to use the given information about the mass of the metal and the heat released during the reaction.
First, we need to calculate the moles of the metal (M). We can do this by dividing the mass of the metal by its molar mass. The molar mass of an unknown metal will require additional information since we don't have the identity of the metal.
Let's assume we have additional information that allows us to determine the molar mass of metal M. For example, let's say the molar mass of M is 100 g/mol.
Using this information, we can calculate the moles of metal M:
moles of metal M = mass of metal M / molar mass of metal M
= 9.85 g / 100 g/mol
= 0.0985 mol
Next, we need to determine the moles of M2O3 produced in the reaction. From the balanced chemical equation, we can see that the stoichiometric ratio between M and M2O3 is 4:2 or 2:1. This means that for every 2 moles of M, we get 1 mole of M2O3.
Since we have 0.0985 moles of M, we can calculate the moles of M2O3:
moles of M2O3 = moles of M / 2
= 0.0985 mol / 2
= 0.04925 mol
Now, let's calculate the heat released (q) during the reaction. The given information states that 57.8 kJ of heat is liberated during the reaction.
The balanced chemical equation shows that four moles of M produce two moles of M2O3. Since the reaction produces twice the amount of M2O3, the heat released will also be doubled. Therefore, the heat released for 0.04925 moles of M2O3 is:
q = (57.8 kJ / 2) * 0.04925 mol
= 1.41335 kJ
Now that we know the heat released (1.41335 kJ) and the number of moles of M2O3 (0.04925 mol), we can calculate the molar enthalpy change (ΔH) of the reaction:
ΔH = q / moles of M2O3
= 1.41335 kJ / 0.04925 mol
≈ 28.712 kJ/mol
To determine the identity of the metal, we can compare the experimental molar enthalpy change (28.712 kJ/mol) with the known molar enthalpy changes of metal oxides. The molar enthalpy change for M2O3 should match the experimental value closely.
By consulting a reference table or database containing molar enthalpy values for metal oxides, we can find which metal oxide has a molar enthalpy change close to 28.712 kJ/mol. This will help us identify the metal M.