Final answer:
The volume of a balloon filled with 17.8 g of helium can be calculated using the ideal gas law equation. By plugging in the given mass of helium and the molar mass of helium, we can determine the moles of helium. Using the ideal gas law equation and assuming constant temperature and pressure, the volume of the balloon can be calculated to be approximately 10.7 L.
Step-by-step explanation:
To calculate the volume of a balloon filled with helium, we can use the ideal gas law equation:
V = nRT/P
Where V is the volume of the balloon, n is the moles of helium, R is the ideal gas constant, T is the temperature in kelvin, and P is the pressure.
If we assume the temperature and pressure are constant, we can rearrange the equation to solve for V:
V = nRT/P
In this case, we are given the mass of helium (17.8 g), and we can use the molar mass of helium (4.003 g/mol) to calculate the moles of helium using the equation:
n = m/M
Where n is the moles, m is the mass, and M is the molar mass. Plugging in the values, we can calculate the moles of helium:
n = 17.8 g / 4.003 g/mol = 4.446 mol
Using the ideal gas law equation, we can calculate the volume of the balloon:
V = (4.446 mol)(0.0821 L·atm/mol·K)(298 K) / 1.01 atm = 10.7 L
So the balloon would be approximately 10.7 L in size when filled with 17.8 g of helium.