To calculate the density of helium under the given conditions, we can use the ideal gas law equation:
PV = nRT
where: P = pressure (in atmospheres) V = volume (in liters) n = number of moles R = ideal gas constant (0.0821 L·atm/(mol·K)) T = temperature (in Kelvin)
First, let's convert the given temperature from Celsius to Kelvin: T(K) = T(°C) + 273.15 T(K) = 27 + 273.15 T(K) = 300.15 K
Next, we rearrange the ideal gas law equation to solve for the number of moles (n): n = PV / RT
Substituting the given values: P = 3 ATM V is unknown R = 0.0821 L·atm/(mol·K) T = 300.15 K
Now, let's calculate the volume (V) using the ideal gas law equation: V = nRT / P
n = (4 g/mol) / (4 g/mol) (since the atomic mass of helium is 4 g/mol) = 1 mol
V = (1 mol) * (0.0821 L·atm/(mol·K)) * (300.15 K) / (3 ATM) V = 8.2265 L
Now that we have the volume, we can calculate the density (d) of helium using the formula: d = mass / volume
The mass of 1 mole of helium is 4 grams, so: d = (4 g) / (8.2265 L) d ≈ 0.485 g/L
Therefore, the density of helium under the given conditions is approximately 0.485 g/L.