How is the Rate of Appearance of H2 Related to the Rate of Disappearance of Fe?

If you are wondering how the rate of appearance of hydrogen gas (H2) is related to the rate of disappearance of iron (Fe) in a chemical reaction, this article will help you understand the concept of reaction rates and stoichiometry. 

What is Reaction Rate?

Reaction rate is a measure of how fast a chemical reaction occurs. It is usually expressed as the change in concentration of a reactant or product over a certain amount of time. For example, if we have a reaction:

$$A + B \rightarrow C + D$$

The rate of disappearance of A can be written as:

$$-\frac{\Delta [A]}{\Delta t}$$

Where $\Delta [A]$ is the change in concentration of A and $\Delta t$ is the change in time. The negative sign indicates that the concentration of A decreases over time.

Similarly, the rate of appearance of C can be written as:

$$\frac{\Delta [C]}{\Delta t}$$

Where $\Delta [C]$ is the change in concentration of C and $\Delta t$ is the change in time. The positive sign indicates that the concentration of C increases over time.

What is Stoichiometry?

Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It is based on the principle of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Therefore, the number of atoms of each element must be the same before and after the reaction.

For example, if we have a reaction:

$$2A + 3B \rightarrow 4C + D$$

We can see that there are 2 atoms of A, 3 atoms of B, 4 atoms of C and 1 atom of D on both sides of the equation. This means that the coefficients (the numbers in front of each compound) represent the mole ratios between the reactants and products. For example, for every 2 moles of A that react, 4 moles of C are produced.

How to Relate Reaction Rates and Stoichiometry?

To relate the reaction rates and stoichiometry, we need to use the mole ratios between the reactants and products. For example, if we have a reaction:

$$2HI(g) \rightarrow H_2(g) + I_2(g)$$

We can see that for every 2 moles of HI that disappear, 1 mole of H2 appears and 1 mole of I2 appears. Therefore, we can write:

$$-\frac{\Delta [HI]}{\Delta t} = \frac{1}{2}\frac{\Delta [H_2]}{\Delta t} = \frac{1}{2}\frac{\Delta [I_2]}{\Delta t}$$

This means that the rate of disappearance of HI is twice that than the rate of appearance of H2 or I2.

Example: How is the Rate of Appearance of H2 Related to the Rate of Disappearance of Fe?

Let’s consider a reaction where iron (Fe) reacts with hydrochloric acid (HCl) to produce hydrogen gas (H2) and iron(II) chloride (FeCl2):

$$Fe(s) + 2HCl(aq) \rightarrow H_2(g) + FeCl_2(aq)$$

We can see that for every 1 mole of Fe that disappears, 1 mole of H2 appears and 1 mole of FeCl2 appears. Therefore, we can write:

$$-\frac{\Delta [Fe]}{\Delta t} = \frac{\Delta [H_2]}{\Delta t} = \frac{\Delta [FeCl_2]}{\Delta t}$$

This means that the rate of disappearance of Fe is equal to the rate of appearance of H2 or FeCl2.

According to Toppr, if the rate of disappearance of Fe is 3 g/min, then the rate of appearance of H2 will be:

$$\frac{\Delta [H_2]}{\Delta t} = -\frac{\Delta [Fe]}{\Delta t} = -(-3 g/min) = 3 g/min$$

However, this answer assumes that the concentration of Fe is measured in grams per liter (g/L), which is not very common for solids. A more accurate way to measure the concentration of Fe is in moles per liter (M), which requires dividing by its molar mass (55.85 g/mol). Therefore, if we convert grams to moles, we get:

$$\frac{\Delta [H_2]}{\Delta t} = -\frac{\Delta [Fe]}{\Delta t} = -(-\frac{3 g}{55.85 g/mol} \frac{1 mol}{L} \frac{1 L}{min}) = 0.054 M/min$$

This means that the concentration of H2 increases by 0.054 M every minute.

Conclusion

In this article, we have learned how to relate the rate of appearance of H2 to the rate of disappearance of Fe in a chemical reaction. We have seen that the reaction rate is the change in concentration of a reactant or product over time, and that stoichiometry is the study of the quantitative relationships between the reactants and products. We have also seen how to use the mole ratios between the reactants and products to write equations that relate their reaction rates. Finally, we have solved an example where we calculated the rate of appearance of H2 given the rate of disappearance of Fe. We hope this article has helped you understand this topic better.

Doms Desk

Leave a Comment