Answer:
1.24 L
Explanation:
Avogadro's Law
[tex]\frac{V_{1} }{n_{1} } = \frac{V_{2} }{n_{2} }[/tex]
Convert 0.590 g of He to moles.
0.590 g x (1 mol/4.00 g) = 0.1475 mol He
Add 0.1475 mol to 0.100 mol since the initial moles (n1) increases by this amount.
0.100 mol + 0.1475 mol = 0.2475 mol He
This will represent the final moles (n2)
The initial volume is given, 0.500 L. Plug in the values.
[tex]\frac{0.500 L}{0.100 mol} = \frac{V_{2} }{0.2465 mol}[/tex]
[tex]V_{2} = \frac{(0.500 L)(0.2475 mol)}{(0.100 mol)} \\V_{2} = 1.2375\\V_{2} = 1.24 L[/tex]
Taking into account the Avogadro's law, the new volume will be 1.24 L.
Avogadro's law establishes the relationship between the amount of gas and its volume when the temperature and pressure are held constant. Remember that the amount of gas is measured in moles.
This law states that constant pressure and temperature, the same amount of gas has the same volume regardless of the chemical element that forms it.
On the other hand, Avogadro's law establishes that the volume is directly proportional to the quantity of gas: if the quantity of gas increases, the volume will increase; whereas if the amount of gas decreases, the volume decreases.
Mathematically, this law states that the ratio between the volume and the quantity of gas is constant:
[tex]\frac{V}{n} =k[/tex]
Assuming that you have an initial state 1 and the conditions are modified to a final state 2, it is true:
[tex]\frac{V1}{n1} =\frac{V2}{n2}[/tex]
In this case, being the molar mass of He 4 g/mole, 0.590 grams of He are contained in the following amount of moles:
[tex]0.590 gramsx\frac{1 mole}{4 grams} =0.1475 moles[/tex]
Then, you know:
Replacing in Avogadro's Law:
[tex]\frac{0.500 L}{0.100 moles} =\frac{V2}{0.2475 moles}[/tex]
Solving:
[tex]V2=0.2475 molesx\frac{0.500 L}{0.100 moles}[/tex]
V2= 1.2375 L≅ 1.24 L
Finally, the new volume will be 1.24 L.
Learn more:
