Final Answer:
The density of krypton at 47°C and 671 mmHg is 2.82 g/L.
Step-by-step explanation:
The density of a gas can be calculated using the ideal gas law:
PV = nRT
where:
P is the pressure (in atm)
V is the volume (in liters)
n is the number of moles of gas
R is the ideal gas constant (0.08206 L·atm/mol·K)
T is the temperature (in Kelvin)
First, we need to convert the pressure from mmHg to atm:
P = (671 mmHg) × (1 atm/760 mmHg) = 0.883 atm
Next, we need to convert the temperature from Celsius to Kelvin:
T = (47°C) + 273.15 = 320.15 K
The molar mass of krypton is 83.798 g/mol.
Now we can plug all of these values into the ideal gas law to solve for the density (ρ):
ρ = n/V = (P/RT) × (M/molar mass)
where:
M is the mass of the gas
m is the molar mass of the gas
ρ = (0.883 atm / (0.08206 L·atm/mol·K) × (320.15 K)) × (83.798 g/mol) = 2.82 g/L
Therefore, the density of krypton at 47°C and 671 mmHg is 2.82 g/L.