(a) Which reaction is spontaneous in the hydrogen fuel cell: hydrogen gas plus oxygen gas makes water, or water makes hydrogen gas plus oxygen gas?

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welcome back everyone. We have a true or false example here in the hydrogen fuel cell. The reaction of hydrogen gas with oxygen that produces water is spontaneous while the reverse reaction is not spontaneous. So we want to recall that our standard cell potential he'd not sell when it's positive. This tells us that our reaction occurs spontaneously. So reaction is spontaneous when we have a standard cell potential that is negative. This tells us that our reaction is non spontaneous And so we're going to write out the half reactions and figure out the standard cell potentials based on what we have written out. So beginning with our reaction, we're told from the prompt that we have hydrogen gas. So H two reacting with oxygen gas to produce water. We need to make sure this reaction is balanced. So we're going to place a coefficient of two in front of our water where we'll now have to have a coefficient of two in front of our hydrogen gas. So this is going to be our overall reaction. Now we don't know our standard cell potential for this reaction. So we need to calculate it and recall that we can calculate it by taking our cell potential of our standard cell potential of our anodes or sorry, of our cathode half reaction, subtracted from the standard cell potential of our an ode half reaction, meaning we need to write out our half reactions as our next step. So for our first half reaction, we have our two moles of hydrogen gas which produces four moles of hydride with the release of four electrons. For our second half reaction, we have our oxygen gas Where on our product side we have two moles of water. Now we need to balance out the second half reaction because we see that on the product side, we have formals of hydride and none on the reactant side. So we're going to expand this reactant side here and add four moles of hydride. We need to make sure that the overall charges are balanced. In our first half reaction we have a net charge of zero on both sides because we have this plus four charge canceled out by the addition of the four electrons. Whereas in our second half reaction we have a net charge of plus four on the reacting side and a net charge of zero on the product side, meaning we're also going to expand this reaction or the reaction side here by adding four electrons as a third reactant. So now we have atoms and charges balanced in both of these half reactions. We next wanna make note of our standard cell potentials for both of these half reactions. For our first half reaction, we recognize that we have electrons on the product side, meaning that this first half reaction occurs as an oxidation, which we recall occurs at the an ode of our voltaic cell. And so we would look up in our text books, the standard cell potential for the oxidation of hydrogen gas and we would see that it has a standard cell potential of zero volts. So 0.0 volts to be specific. Now looking at our second half reaction, we recognize that we have electrons on the reacting side, meaning that this reaction occurs as a reduction, which you recall occurs at the cathode of our voltaic cell. And when we look up the standard cell potential for the reduction of oxygen gas, we see in our textbooks a value of 1.23V now that we know are cathodes and anodes of our half reactions here. We can calculate the standard cell potential for the overall reaction. And so we would say that our standard cell potential for the overall reaction is equal to our self potential of our cathode which we determined to be our second half reaction, being 1.23 volts subtracted from the standard cell potential of our an ode. Being our first half reaction which had a value of zero volts. And this standard cell potential for the overall reaction is going to equal positive 1.23 volts, meaning that this forward reaction is going to be spontaneous meaning we can agree with the first part of our prompt here because it's true so far. So moving on to our reverse reaction, we're just going to flip our half reactions. So for our reverse reaction will now have our four moles of hydride on the reactant side with our four electrons Which produces our two moles of our hydrogen gas. And sorry, this should say Q here. So now we have our electrons here on the react inside, meaning that this reaction will now occur as a reduction which we would recognize as our cathode of our voltaic cell, where we still have that standard cell potential equal to zero volts from our textbooks. Now, for our second half reaction, we're going to also reverse it so that we now have two moles of our liquid water producing as products, one mole of oxygen gas, plus four moles of hydride plus our four electrons. And now we will see that we have electrons on the product side here for this half reaction, meaning that this reaction occurs as an oxidation, meaning that we recognize this as our An ode of our voltaic cell. And we will see that we have a standard cell potential still equal according to our text books of 1.23V. And so now calculating for our overall standard cell potential for the reverse reaction, we're going to have the difference between our cell potential of our cathode which we determined is going to be zero volts subtracted from our cell potential of our an ode half reaction, which we determined is 1.23 volts and this is equal to a negative value being negative, 1.23 volts for the overall standard cell potential of the reverse reaction. Because we see that this value is negative. This tells us that the reaction is non spontaneous in the reverse direction and going back to our prompt. That is exactly what the prompt also states, meaning that we would agree with this as true. So overall our final answer is going to be that the given statement is a true statement. I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

(a) Which reaction is spontaneous in the hydrogen fuel cell: hydrogen gas plus oxygen gas makes water, or water makes hydrogen gas plus oxygen gas?

Verified Solution

Key Concepts

Spontaneity of Reactions

Gibbs Free Energy

Electrochemical Reactions