Final answer:
To calculate the amount of gas added when a balloon is expanded, we use Avogadro's law, specifically the equation n2 = (V2 × n1) / V1. This gives us the total moles of gas after expansion, from which we subtract the original moles to find the added amount.
Step-by-step explanation:
To find the amount of gas added when a balloon expands, we can use the relationship between the initial and final conditions of the gas, assuming that the temperature and pressure remain constant. The correct equation from the options provided is: n2 = (V2 × n1) / V1. This equation is derived from the combined gas law, which in this case simplifies to Avogadro's law stating that volume and amount (number of moles) of gas are directly proportional if pressure and temperature are held constant. So, using our given values, the initial number of moles (n1) is 0.040 mol and the initial volume (V1) is 5.0 mL, which we convert to liters (0.005 L), and the expanded volume (V2) is 1.0 L. Substituting into the equation:
n2 = (1.0 L × 0.040 mol) / 0.005 L
This would give us the total number of moles of gas present in the balloon after expansion, to then determine the amount of gas added we subtract the original moles (n1) from the total moles (n2).