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A mixture of 1 kmol of hydrogen (H2) and n kmol of oxygen (O2), initially at 25°C and 1 atm, burns completely in a closed, rigid, insulated container. The container finally holds a mixture of water vapor and O2 at 2000 K. The ideal gas model applies to each mixture and there is no change in kinetic or potential energy between the initial and final states. Determine: (a) the value of n. (b) the final pressure, in atm.

Respuesta :

Answer:

a) [tex]n_{H_{2}}=0\\n_{O_{2}}=0.5\\n_{H_{2}O}=1[/tex]

b) [tex]P_{2}=5.02 atm[/tex]

Explanation:

First we set the equation for this reaction:

[tex]2H_{2}+O_{2} \longrightarrow 2H_{2}O[/tex]

As we can see, we need 2 kmol of hydrogen per mol of oxygen, therefore, only 0.5 kmol of oxygen will react, so the equation, for this situation, is the following:

[tex]H_{2}+0.5O_{2} \longrightarrow H_{2}O[/tex]

Now we know the value of n for each component of the reaction:

[tex]n_{H_{2}}=0\\n_{O_{2}}=0.5\\n_{H_{2}O}=1[/tex]

With this information we can calculate the value of the pressure knowing that the volume is constant, so we calculate the volume at the beginning and then with that value, the final pressure with the ideal gas law:

[tex]PV=nRT\\R=8.2x10^{-5} \frac{atm*L}{kmol*K} \\\\V=\frac{n_{1}RT_{1}}{P_{1}} =0.049L\\\\P_{2}=\frac{n_{2}RT_{2}}{V}=5.02 atm[/tex]