A mixture of 2.0 mol H2 and 1.0 mol of O2 is placed in a sealed evacuated container made of a perfect insulating material at 28C. The mixture is ignited with a spark and it reacts to form liquid water. What is the final temperature of the water

To find the final temperature of the water formed after the reaction, we can use the concept of Hess's Law and the information given in the question.

First, we need to determine the stoichiometry of the reaction. From the balanced equation for the reaction of hydrogen and oxygen to form water, we know that:

2H2 + O2 -> 2H2O

According to the stoichiometry, 2 moles of H2 react with 1 mole of O2 to form 2 moles of H2O.

Now, let's calculate the total moles of water formed in the reaction:
Since each mole of O2 reacts with 2 moles of H2, the limiting reactant in this case is O2. Therefore, we have 1 mole of O2 reacting to form 2 moles of H2O.

Since each mole of water has a molar mass of approximately 18 g/mol, we can calculate the mass of water formed in the reaction:
Mass of Water = 2 moles of H2O * 18 g/mol = 36 g

To find the heat released (or absorbed) during the reaction, we can use the equation:

q = m * ΔT * C

Where:
q is the heat released or absorbed (in this case, released),
m is the mass of the water formed (36 g),
ΔT is the change in temperature,
C is the specific heat capacity of water (4.18 J/g°C).

Since the container is perfectly insulated and there is no heat exchange with the surroundings, the heat released by the reaction will be equal to the heat absorbed by the water. Therefore, the equation becomes:

q = 0 (no heat exchange with surroundings) = (36 g) * ΔT * (4.18 J/g°C)

Rearranging the equation, we can solve for ΔT:

ΔT = 0 / (36 g * 4.18 J/g°C)

ΔT = 0 (no temperature change)

Therefore, the final temperature of the water will be the same as the initial temperature, which is 28°C.

To determine the final temperature of the water formed after the reaction, we can apply the principle of conservation of energy.

The reaction between hydrogen (H2) and oxygen (O2) to form water is highly exothermic, meaning it releases heat. The heat released during the reaction will raise the temperature of the products, in this case, the water.

To find the final temperature, we need to consider the heat released during the reaction and the heat capacity of the water formed. The heat capacity (C) represents the amount of heat required to raise the temperature of a substance by 1 degree Celsius.

In this case, we know the initial temperature (28°C), the number of moles of reactants (2.0 mol H2 and 1.0 mol O2), and the heat released during the reaction.

First, let's calculate the heat released during the reaction. The balanced chemical equation for the reaction is:

2H2(g) + O2(g) -> 2H2O(l)

According to the stoichiometry of the equation, every 2 moles of H2 reacted with 1 mole of O2 to form 2 moles of H2O. Therefore, the heat released during the reaction can be calculated using the enthalpy change of formation (ΔHf) for water.

ΔHf(H2O) = -286 kJ/mol (heat of formation of water)

The heat released during the reaction can be calculated as follows:

Heat released (q) = ΔHf(H2O) * moles of H2O formed

Since every 2 moles of H2 reacted to form 2 moles of H2O, the moles of H2O formed is equal to the moles of H2 reacted. Therefore, the heat released can be calculated as:

q = ΔHf(H2O) * moles of H2

q = -286 kJ/mol * 2.0 mol

Now we have the total heat released during the reaction. To calculate the final temperature of the water, we need to consider the heat capacity of water. The heat capacity of water is approximately 4.18 J/g°C.

Next, we need to calculate the mass of water formed. To do this, we can use the molar mass of water, which is approximately 18 g/mol.

Mass of water formed = moles of H2O formed * molar mass of water

Since every 2 moles of H2 reacted to form 2 moles of H2O, the moles of H2O formed is equal to the moles of H2 reacted. Therefore, the mass of water formed can be calculated as:

Mass of water formed = moles of H2 * molar mass of water

Mass of water formed = 2.0 mol * 18 g/mol

Once we have the mass of the water, we can calculate the heat absorbed by the water using the relationship:

Heat absorbed = mass of water formed * heat capacity of water * ΔT

Where ΔT is the change in temperature.

Since the water forms at the same temperature as the reactants (28°C), the initial temperature of the water is also 28°C.

Now we can rearrange the equation to solve for ΔT:

ΔT = Heat absorbed / (mass of water formed * heat capacity of water)

Plugging in the values we obtained earlier:

ΔT = (q) / (mass of water formed * heat capacity of water)

Therefore, by calculating this expression, we can determine the final temperature of the water formed.

2H2 + O2 ==> 2H2O

2 moles H2 and 1 mol O2 will form 2 moles H2O or 2*18.015 grams. I looked up delta Ho in my text and found that it releases 187.8 kJ/mol which will be 375,600 J/ 2 moles or 36.03 grams H2O.
375,600 = mass water x specific heat water x (Tfinal-Tinitial).
Solve for Tf. Check my thinking. When you finish (be prepared for a shock), check your work and see if
mass water x specific heat water (Tf-28) = the heat released.
I presume that we neglect that this temperature should vaporize the water.