1. the molar mass of helium is 4.00 g/mol.
calculate the volume of 1 mol of helium at STP (T = 273, P = 1 atm)
what is the density of helium at STP?
2. the density of an ideal gas is 1.35 kg/m^3. if the temperature is Kelvin and the pressure are both doubled, find the new density of the gas.
see above
To calculate the volume of 1 mole of helium at STP, we can use the ideal gas equation:
PV = nRT
Where:
P = Pressure (1 atm)
V = Volume of the gas
n = Number of moles (1 mol)
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature (273 K at STP)
Rearranging the equation to solve for V, we have:
V = (nRT) / P
Plugging in the values, we get:
V = (1 mol)(0.0821 L·atm/(mol·K))(273 K) / (1 atm)
Calculating this, we find:
V ≈ 22.4 L
So, the volume of 1 mole of helium at STP is approximately 22.4 liters.
To find the density of helium at STP, we first need to calculate the mass of 1 mole of helium. The molar mass of helium is given as 4.00 g/mol. Therefore, the mass of 1 mole of helium is also 4.00 grams.
Now, we can use the formula for density:
Density = Mass / Volume
Plugging in the values we have:
Density = 4.00 g / 22.4 L
Calculating this, we find:
Density ≈ 0.18 g/L
Thus, the density of helium at STP is approximately 0.18 grams per liter.
Moving on to the second question:
If the density of an ideal gas is given as 1.35 kg/m^3 and both the temperature and pressure are doubled, we can use the relationship between density and pressure:
Density1 / Density2 = Pressure2 / Pressure1
Since the pressure is doubled, Pressure2 = 2 * Pressure1.
Plugging in the values we have:
1.35 kg/m^3 / Density2 = 2 * Pressure1 / Pressure1
Simplifying the equation, we get:
Density2 = 1.35 kg/m^3 / 2
Calculating this, we find:
Density2 = 0.675 kg/m^3
Therefore, the new density of the gas, when both temperature and pressure are doubled, is 0.675 kg/m^3.