If 3.00 mol
of an ideal gas at STP were confined to a cube, what would be the length in cm
of an edge of this cube?
To find the length of the edge of the cube, we need to find the volume of the cube first using the ideal gas law and then calculate the length of one side of the cube.
Given:
- moles of gas (n) = 3.00 mol
- temperature (T) = 273 K (STP)
- pressure (P) = 1 atm (STP)
- gas constant (R) = 0.0821 L.atm/mol.K
The ideal gas law is given by: PV = nRT
V = nRT/P
V = (3.00 mol)(0.0821 L.atm/mol.K)(273 K)/(1 atm)
V = 6.28 L
Since the gas is confined to a cube, the volume of the cube would be V = x^3, where x is the edge length of the cube.
Therefore, 6.28 L = x^3
x = (6.28 L)^(1/3) = 1.84 L
To convert liters to cm, we can use the fact that 1 L = 1000 cm^3
Therefore, 1.84 L = 1840 cm^3
Now we need to find the length of one edge of the cube. Since the cube has 3 edges, each edge would be x = 1840^(1/3) cm
x ≈ 12.4 cm
Therefore, the length of the edge of the cube would be approximately 12.4 cm.