Final answer:
The length of the side of a cube that would contain 6 g of helium gas at STP is approximately 32.2 cm after calculating the volume of the gas at these conditions.
Step-by-step explanation:
To calculate the volume of the gas at standard temperature and pressure (STP), we first find the volume of liquid helium using the given density. Next, we use the molar volume at STP, which is 22.4 liters per mole of gas, to find the volume of the helium gas. Lastly, we can determine the side of the cube that would contain this volume.
First, calculate the volume of liquid helium using its density:
V = Øm/Ø
h = Ømass/density = 6 g / 0.125 g/cm³ = 48 cm³
Since one mole of any gas at STP occupies 22.4 liters, we can convert the volume of liquid helium to its gaseous volume at STP. Knowing that the molar mass of helium is approximately 4 g/mol, we calculate the number of moles of helium:
n = Ømass / molar mass = 6 g / 4 g/mol = 1.5 mol
The total volume of helium gas at STP is therefore:
V = n × Ø22.4 L/mol = 1.5 mol × 22.4 L/mol = 33.6 L
Since 1 L = 1,000 cm³, the volume in cubic centimeters is:
V = 33.6 L × 1,000 cm³/L = 33,600 cm³
Lastly, we find the length of a side of a cube that has this volume:
s = ØV¹³ = Ø33,600 cm³¹³ ≈ 32.2 cm
Therefore, the length of the side of a cube containing the helium gas at STP is approximately 32.2 cm.