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Chapter 5: Problem 43

An \(11.2-\mathrm{L}\) sample of gas is determined to contain \(0.50 \mathrm{~mol} \mathrm{~N}_{2}\). At the same temperature and pressure, how many moles of gas would there be in a 20.-L sample?

Short Answer

Expert verified
At the same temperature and pressure, there would be approximately \(0.89 \,\text{mol}\) of gas in the 20-L sample.

Step by step solution

01

Understand the avogadro's law

Avogadro's law says that for an ideal gas, at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of the gas. Mathematically, it can be represented as: \[ \frac{V_1}{n_1} = \frac{V_2}{n_2} \] Here, \(V_1\) and \(V_2\) are the volumes of the gas, and \(n_1\) and \(n_2\) are the number of moles in the respective volumes at the same temperature and pressure.
02

Find the unknown using given values

Now we have all the values required to solve for the unknown number of moles in the 20-L sample. Substitute the known values in the equation and solve for \(n_2\): \[ \frac{11.2\,\text{L}}{0.50\,\text{mol}} = \frac{20\,\text{L}}{n_2} \]
03

Solve for n2

Now, rearrange the equation and solve for \(n_2\): \[ n_2 = \frac{20\,\text{L} \times 0.50\,\text{mol}}{11.2\,\text{L}} \]
04

Calculate the number of moles

Perform the calculation to find the number of moles in the 20-L sample: \[ n_2 = \frac{10}{11.2} \] \[ n_2 \approx 0.89\,\text{mol} \] So, there would be approximately 0.89 moles of gas in the 20-L sample at the same temperature and pressure.

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Most popular questions from this chapter

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