Question

which statement is true about 22.4 l each of hydrogen, ammonia, and uranium dioxide gas assuming that the temperature and pressure are the same for all of gases?

hydrogen gas has the least number of molecules.

the gases have the same number of molecules.

oxygen gas has the most number of molecules.

uranium dioxide gas has the most number of molecules.

Explanation:

Step1: Recall Avogadro's Law

Avogadro's Law states that \( V = kn\) (where \( V\) is volume, \( k\) is a constant, and \( n\) is the number of moles). At the same temperature (\( T\)) and pressure (\( P\)), for gases, if \( V_1=V_2\), then \( n_1 = n_2\).

Step2: Relate moles to number of molecules

The number of molecules \( N=nN_A\) (where \( N_A\) is Avogadro's number, \( N_A = 6.022\times10^{23}\text{ mol}^{-1}\)). Since \( n\) (number of moles) is the same for the three gases (because \( V\), \( T\), and \( P\) are the same, from Avogadro's Law) and \( N_A\) is a constant, the number of molecules \( N\) is the same for all three gases.

Answer:

The gases have the same number of molecules.