Respuesta :
Answer:
[tex]C_{p}= \frac{15.82}{m_{calorimeter}}\\\\c_{p}=7.64 kJ/gK[/tex]
Explanation:
First we set the equation for the combustion:
[tex]C_{(s)}+O_{2}_{(g)} \longrightarrow CO_{2}_{(g)}[/tex]
As the equation is already balanced, we just need to look at the coefficients, that are 1 for all the elements of the reaction, so 1 mole of carbon produces 1 mole of carbon dioxide. Now we need to find how many moles are 0.5662 g of carbon:
[tex]M_{C}=12.01 g/mole\\n_{C}=m_{C}/M_{C}\\n_{C}=0.047mole[/tex]
Know we proceed to know how many moles of carbon dioxide were produced. As we know the reaction is 1:1, the moles of carbon dioxide are 0.047.
Now we need to know the mass of the carbon dioxide produced:
[tex]M_{CO_{2}}=44.01g/mole\\m_{CO_{2}}=M_{CO_{2}}*n_{CO_{2}}\\m_{CO_{2}}=2.07g[/tex]
From literature we find that the enthalpy of formation of carbon dioxide is -393.5 kJ/mole. We need it in terms of mass, so we convert it with the molar mass as follows:
[tex]-393.5kJ/mole * M_{CO_{2}}=-8.94kJ/g[/tex]
With this we can continue with the calculation given the equation Q=q*m
So Q=18.51 kJ
To calculate the heat capacity we use Q=mCpΔT, therefore:
[tex]C_{p}=\frac{Q}{m*\Delta T} \\\\C_{p}=\frac{18.51}{m*1.19}=\frac{15.82}{m_{calorimeter}}[/tex]
As we don't know the mass of the calorimeter, we just leave the specific heat capacity as follows:
[tex]c_{p}=\frac{q}{\Delta T}\\\\q=8.94kJ\\\Delta T=1.19\\c_{p}=7.64 kJ/gK[/tex]
