Question

Given an 11.2-L sample of argon containing 0.450 mol of gas, determine the number of moles of nitrogen present in a 29.4-L sample of nitrogen at the same temperature and pressure.

Answer 1

Using the ideal gas law and Avogadro's law, we determine that there are 1.18 moles of nitrogen present in a 29.4-L sample of nitrogen at the same temperature and pressure.

Step-by-step explanation:

The student's question involves using the ideal gas law to determine the number of moles in a given volume of nitrogen at constant temperature and pressure, assuming that both argon and nitrogen behave as ideal gases. To find the number of moles of nitrogen, we use the relationship that at the same temperature and pressure, equal volumes of gases contain the same number of moles (Avogadro's law). We know that an 11.2-L sample of argon contains 0.450 mol of gas. Therefore, using the proportional relationship between volume and moles, we can set up a ratio:

0.450 mol Ar / 11.2 L Ar = x mol N2 / 29.4 L N2

Solving for x (the moles of nitrogen), we get:

x mol N2 = (0.450 mol Ar * 29.4 L N2) / 11.2 L Ar

x mol N2 = 1.18 mol N2

Therefore, there are 1.18 moles of nitrogen in a 29.4-L sample of nitrogen at the same temperature and pressure.