at 20 C the vapor pressure of dry ice is 56.5 atm. if 32 g of dry ice is placed in an evacuated .25 l chamber at a constant temperature of 20 C will all the dry ice sublime
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To determine if all the dry ice will sublime in the given conditions, we need to compare the vapor pressure of dry ice at 20°C to the pressure inside the chamber.
To begin, let's assume that ideal gas laws apply to the carbon dioxide gas released from the dry ice during sublimation. The ideal gas law equation is:
PV = nRT
Where:
P is the pressure (in atmospheres)
V is the volume (in liters)
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature (in Kelvin)
Let's convert the given temperature of 20°C to Kelvin:
T = 20°C + 273.15 = 293.15 K
We know that 32 g of dry ice is placed in a 0.25 L chamber, so our variables are:
P (pressure) = ?
V (volume) = 0.25 L
n (number of moles) = to be determined
R (ideal gas constant) = 0.0821 L·atm/(mol·K)
T (temperature) = 293.15 K
First, we need to find the number of moles (n) of carbon dioxide (CO2) in 32 g of dry ice. To do this, we'll use the molar mass of CO2, which is approximately 44 g/mol.
n = mass / molar mass
n = 32 g / 44 g/mol
n ≈ 0.7272 mol
Now, we can rearrange the ideal gas law equation to solve for pressure (P):
P = nRT / V
Plugging in the values:
P = (0.7272 mol) * (0.0821 L·atm/(mol·K)) * (293.15 K) / (0.25 L)
P ≈ 80.4 atm
Since the vapor pressure of dry ice at 20°C is 56.5 atm, and the calculated pressure inside the chamber is approximately 80.4 atm, it means that all the dry ice will indeed sublime. The pressure inside the chamber is higher than the vapor pressure of dry ice at that temperature, causing the dry ice to turn directly into gas (sublime) until the pressures equalize.