Final answer:
To find the number of atoms of helium gas in a spherical balloon, we can use the ideal gas law equation PV = nRT. By rearranging the equation and plugging in the given values, we can calculate the number of moles of helium gas in the balloon. Finally, by multiplying the number of moles by Avogadro's number, we can determine the number of atoms.
Step-by-step explanation:
To determine the number of atoms of helium gas that fill a spherical balloon, we need to use the ideal gas law equation. The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in kelvin. We can rearrange this equation to solve for n, the number of moles. n = PV / RT.
First, we need to convert the diameter of the balloon to radius by dividing it by 2: 29.8 cm / 2 = 14.9 cm = 0.149 m.
Using the formula for the volume of a sphere, V = (4/3)πr^3, we can calculate the volume of the balloon: V = (4/3)π(0.149 m)^3 = 0.537 L.
Next, we need to convert the temperature to kelvin by adding 273.15: 19.0°C + 273.15 = 292.15 K.
Plugging in the values into the ideal gas law equation, we get n = (1.00 atm)(0.537 L) / (0.0821 L•atm/mol•K)(292.15 K) = 0.00984 mol.
Finally, we can calculate the number of atoms by multiplying the number of moles by Avogadro's number, which is 6.022 x 10^23 atoms/mol. Number of atoms = (0.00984 mol)(6.022 x 10^23 atoms/mol) = 5.925 x 10^21 atoms.