Answer:
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<u>Answer:</u> The equilibrium concentration of 
is 1.285 M.
<u>Explanation:</u>
The chemical equation for the decomposition of phosphorus pentachloride follows:
The expression for equilibrium constant is given as:
![K_c=\frac{[PCl_3][Cl_2]}{[PCl_5]}](https://tex.z-dn.net/?f=K_c%3D%5Cfrac%7B%5BPCl_3%5D%5BCl_2%5D%7D%7B%5BPCl_5%5D%7D)
We are given:
![[PCl_3]=0.18M](https://tex.z-dn.net/?f=%5BPCl_3%5D%3D0.18M)
![[Cl_2]=0.30M](https://tex.z-dn.net/?f=%5BCl_2%5D%3D0.30M)
The concentration of solid substances are taken to be 1. Thus, they do not appear in the equilibrium constant expression.
Putting values in above equation, we get:
![0.042=\frac{0.18\times 0.30}{[PCl_5]}](https://tex.z-dn.net/?f=0.042%3D%5Cfrac%7B0.18%5Ctimes%200.30%7D%7B%5BPCl_5%5D%7D)
![[PCl_5]=1.285](https://tex.z-dn.net/?f=%5BPCl_5%5D%3D1.285)
Hence, the equilibrium concentration of is 1.285 M.
Answer:
H₂O is the limiting reactant
Theoretical yield of 240 g Al₂O₃ and 14 g H₂
Explanation:
Find how many moles of one reactant is needed to completely react with the other.
6.5 mol Al × (3 mol H₂O / 2 mol Al) = 9.75 mol H₂O
We need 9.75 mol of H₂O to completely react with 6.5 mol of Al. But we only have 7.2 mol of H₂O. Therefore, H₂O is the limiting reactant.
Now find the theoretical yield:
7.2 mol H₂O × (1 mol Al₂O₃ / 3 mol H₂O) × (102 g Al₂O₃ / mol Al₂O₃) ≈ 240 g Al₂O₃
7.2 mol H₂O × (3 mol H₂ / 3 mol H₂O) × (2 g H₂ / mol H₂) ≈ 14 g H₂
Since the data was given to two significant figures, we must round our answer to two significant figures as well.
The heat from the hotter water will go into the colder water untl equilibrium is reached. Equilibrium is same temperature!
Now, the heat is proportional to the mass, the specific heat and the temperature difference. The specific heat does not matter since all is water, it will cancel out:
m_1 * c_H20 * ( T_final - T_1 ) = -m_2 * c_H20 * ( T_final - T_2)
Notice the minus, because one wins the heat of the one who loses it. In this way both sides have the same sign:
m_1*(T_final - T_1)=-m_2*(T_final-T_2), or after some simple algebra:
T_final = (m_1 * T_1 + m_2 * T_2 )/(m_1+m_2),
which looks like an arithmetic mean, and one could have gone for this, but the above shows all the work. Notice that if T_1=T_2, T_final=T_1 always, which makes sense.
Now you can convert volume to mass with the density, but since mass = density*volume and it is all water, the density will cancel out and you can work with volumes. If you prefer just say: 120 ml->120 g , etc ...
T_final = (120*95+320*25)/(320+120)=44.0909 degrees Celsius, or ~ 44.09 degrees with two decimal precision as your statement (beware of precision always!).
