Question

an open flask sitting in a lab refrigerator looks empty, but it is actually filled with a mixture of gases called air. if the flask volume is 4.50 l, and the air is at standard temperature and pressure, how many gaseous molecules does the flask contain? number of gaseous molecules:

Explanation:

Step1: Calculate the number of moles

At standard temperature and pressure (STP: \(T = 273\space K\), \(P= 1\space atm\)), the ideal gas law is \(PV=nRT\), where \(R = 0.0821\space L\cdot atm/(mol\cdot K)\).
We can solve for \(n\) (number of moles) as \(n=\frac{PV}{RT}\).
Substituting \(P = 1\space atm\), \(V=4.50\space L\), \(R = 0.0821\space L\cdot atm/(mol\cdot K)\), \(T = 273\space K\)

$$n=\frac{1\times4.50}{0.0821\times273}$$

$$n=\frac{4.50}{22.4133}\approx0.201\space mol$$

Step2: Calculate the number of molecules

We use Avogadro's number \(N_A=6.022\times 10^{23}\space molecules/mol\)
The number of molecules \(N=n\times N_A\)
Substituting \(n = 0.201\space mol\) and \(N_A=6.022\times 10^{23}\space molecules/mol\)

$$N=0.201\times6.022\times 10^{23}$$

$$N = 1.21\times10^{23}\space molecules$$

Answer:

\(1.21\times 10^{23}\)