Hydrogen gas is filled in a 224 ml glass container at 0 degree celcius and 1 atmospheric pressure. What are the number of molecule of hydrogen in the container??

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18-07-2019
Chemistry

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Hydrogen gas is filled in a 224 ml glass container at 0 degree celcius and 1 atmospheric pressure. What are the number of molecule of hydrogen in the container??

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znk znk · Answer 1 · 2019-07-18T18:08:35+02:00

Answer:

[tex]\boxed{\text{6.02 $\math{\times 10^{21}}$ molecules}}[/tex]

Explanation:

A pressure of 1 atm and a temperature of 0 °C is the old definition of STP. Under these conditions, 1 mol of a gas occupies 22.4 L.

1. Calculate the moles of hydrogen.

[tex]n = \text{0.224 L} \times \dfrac{\text{1 mol}}{\text{22.4 L}} = \text{0.0100 mol}[/tex]

2. Calculate the number of molecules

[tex]\text{No. of molecules} = \text{0.0100 mol} \times \dfrac{\text{6.022 $\times 10^{23}$ molecules}}{\text{1 mol}}\\\\= \textbf{6.02 $\mathbf{\times 10^{21}}$ molecules}\\\\\text{The sample contains }\boxed{\textbf{6.02 $\mathbf{\times 10^{21}}$ molecules}}[/tex]

mariejoepagaduan mariejoepagaduan · Answer 2 · 2019-07-18T18:35:47+02:00

Answer: 6.02 × [tex]10^{21}[/tex] molecules of hydrogen are in the container. The Ideal Gas Law equation gives the relationship among the pressure, volume, temperature, and moles of gas. Once the moles of gas is determined, we use Avogadro's number, 6.022 × [tex]10^{23}[/tex] to get he number of molecules.

Further Explanation:

The Ideal Gas Equation is:

[tex]PV = nRT[/tex]

where:

P - pressure (in atm)

V - volume (in L)

n - amount of gas (in moles)

R - universal gas constant [tex]0.08206 \frac{L-atm}{mol-K}[/tex]

T - temperature (in K)

In the problem, we are given the values:

P = 1 atm

V = 224 mL = 0.224 L (3 significant figures)

n = ?

T = 0 degrees Celsius

We need to convert the temperature to Kelvin before we can use the Ideal Gas Equation. The formula to convert from degree Celsius to Kelvin is:

[tex]Temperature \ in \ Kelvin = Temperature\ in \ Celsius \ + \ 273.15[/tex]

Therefore, for this problem,

[tex]Temperature\ in \ K = 0 +273.15\\Temperature\ in \ K = 273.15[/tex]

Solving for n using the Ideal Gas Equation:

[tex]n \ = \frac{PV}{RT}\\n \ = \frac{(1 \ atm) \ (0.224 \ L)}{(0.08206 \ \frac{L-atm}{mol-K})( 273.15 \ K)} \\ n \ = 9.99\ X \ 10^{-3} mol[/tex]

Now that we know the number of moles of hydrogen gas, we can determine how many molecules there are:

[tex]no.\ of \ molecules \ = moles \ of \ hydrogen \ (\frac{6.022 \ X \ 10^{23} molecules}{1 \ mole\ of \ hydrogen} )\\no.\ of \ molecules \ = 9.99 \ X \ 10^{-3} \ moles \ (\frac{6.022 \ X \ 10^{23} molecules}{1 \ mole\ of \ hydrogen} )\\ no. \ of \ molecules \ = 6.02 \ X 10^{21} \ molecules \ of \ hydrogen[/tex]