Considering the ideal gas law, the volume of 1.2 moles of the sample will be 2.4 L.
An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:
P× V = n× R× T
So, the [tex]\frac{V}{n}[/tex] ratio can be expressed as:
[tex]\frac{V}{n}=\frac{RxT}{P}[/tex]
Being R, P nd T constants in this case, and studying two different states, an initial state 1 and a final state 2, it is satisfied:
[tex]\frac{V1}{n1}=\frac{V2}{n2}[/tex]
In this case, you know:
- V1= 1.5 L
- n1= 0.75 moles
- V2= ?
- n2= 1.2 moles
Replacing:
[tex]\frac{1.5 L}{0.75 moles}=\frac{V2}{1.2 moles}[/tex]
Solving:
[tex]\frac{1.5 L}{0.75 moles}x1.2 moles=V2[/tex]
2.4 L= V2
Finally, the volume of 1.2 moles of the sample will be 2.4 L.
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