4. A balloon contains 2 moles of helium gas with a volume of 4 liters. If more helium is added so that there are now 6 moles of gas (while keeping the temperature and pressure the same), wha will be the new volume of the balloon?

## Step 1<br />The problem involves the application of Avogadro's Law, which states that the volume of a gas is directly proportional to the number of moles of the gas, provided the temperature and pressure are constant. This relationship can be expressed as:<br />### \(V_1/n_1 = V_2/n_2\)<br />where \(V_1\) and \(n_1\) are the initial volume and number of moles, and \(V_2\) and \(n_2\) are the final volume and number of moles, respectively.<br /><br />## Step 2<br />In this problem, the initial volume \(V_1\) is 4 liters and the initial number of moles \(n_1\) is 2 moles. The final number of moles \(n_2\) is 6 moles. We are asked to find the final volume \(V_2\).<br /><br />## Step 3<br />We can rearrange the formula to solve for \(V_2\):<br />### \(V_2 = V_1 \times \frac{n_2}{n_1}\)<br /><br />## Step 4<br />Substitute the given values into the formula:<br />### \(V_2 = 4 \, \text{liters} \times \frac{6 \, \text{moles}}{2 \, \text{moles}}\)<br /><br />## Step 5<br />Calculate the final volume:<br />### \(V_2 = 12 \, \text{liters}\)