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Chapter 5: Problem 50

Consider the following chemical equation. $$2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$$ If 25.0 \(\mathrm{mL}\) \(\mathrm{NO}_{2}\) gas is completely converted to \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas under the same conditions, what volume will the \(\mathrm{N}_{2} \mathrm{O}_{4}\) occupy?

Short Answer

Expert verified
The volume of N₂O₄ gas formed when 25.0 mL of NO₂ gas is completely converted under the same conditions is 12.5 mL.

Step by step solution

01

Find moles of NO₂ gas

First, we need to find the number of moles of NO₂ using the volume given. Since the gas conditions are the same, we can assume equal molar volumes for the two gases. We will use the formula: Number of moles (NO₂) = \(\frac{Volume\: of\: NO₂}{Molar\: Volume}\) However, we don't have the molar volume, so let's substitute it with a variable m: Number of moles (NO₂) = \(\frac{25.0}{m}\)
02

Find moles of N₂O₄ gas

Now, we need to find the number of moles of N₂O₄ using stoichiometry, which is the mole ratio between NO₂ and N₂O₄ in the balanced equation. The balanced equation is: $$2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$$ Based on the stoichiometry, 2 moles of NO₂ produce 1 mole of N₂O₄. So the mole ratio is 2:1. Number of moles (N₂O₄) = \(\frac{Number\: of\: moles\: (NO₂)}{2}\) Now, substitute the value we found in Step 1 for moles of NO₂: Number of moles (N₂O₄) = \(\frac{\frac{25.0}{m}}{2}\)
03

Find the volume of N₂O₄ gas

To find the volume of N₂O₄ gas, we will use the same formula that we used to find the moles of NO₂: Number of moles (N₂O₄) = \(\frac{Volume\: of\: N₂O₄}{Molar\: Volume}\) Now, we can set up the equation as follows: \(\frac{\frac{25.0}{m}}{2} = \frac{Volume\: of\: N₂O₄}{m}\) We can solve for the volume of N₂O₄ by multiplying both sides by the molar volume (m): \(\frac{25.0}{2} = Volume\: of\: N₂O₄\)
04

Calculate the volume of N₂O₄ gas

Now we can simply calculate the volume of N₂O₄ gas: Volume of N₂O₄ = \(\frac{25.0}{2} = 12.5 \mathrm{mL}\) The resulting volume of N₂O₄ gas is 12.5 mL.

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