A piece of solid carbon dioxide, with a mass of 6.8 g, is placed in a 4.0-L otherwise empty container at 21°C.
And your question is?
To find out what happens when the piece of solid carbon dioxide is placed in the empty container at 21°C, we need to understand the concept of sublimation.
Sublimation is the process where a solid substance directly changes into a gas without passing through the liquid state. In the case of carbon dioxide, solid carbon dioxide (also known as dry ice) sublimes when exposed to ambient temperatures.
Here's how you can analyze the situation step by step:
Step 1: Calculate the number of moles of solid carbon dioxide.
To do this, we use the formula:
moles = mass / molar mass
The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.
Substituting the given values:
moles = 6.8 g / 44.01 g/mol
Step 2: Calculate the volume occupied by the gaseous carbon dioxide.
Now that we have the number of moles, we can use the ideal gas law to determine the volume of carbon dioxide gas.
The ideal gas law is given by:
PV = nRT
Where:
P is the pressure (which is not given),
V is the volume (4.0 L),
n is the number of moles (calculated in step 1),
R is the ideal gas constant (approximately 0.0821 L·atm/(mol·K)),
T is the temperature (21°C = 294 K).
Rearranging the formula:
V = (nRT) / P
Since the pressure (P) is not given, we cannot calculate the volume with certainty.
Step 3: Describe the process that will occur.
When the solid carbon dioxide is placed in the container, it will sublime, converting directly from a solid to a gas without passing through the liquid state. The resulting carbon dioxide gas will occupy a larger volume than the initial solid.
However, without knowing the pressure of the system, we cannot accurately calculate the resulting volume of the gas.
In practical terms, what will happen is that the solid carbon dioxide will start to turn into gas, resulting in the formation of a white cloud (due to the low temperature of the gas) and an increase in pressure inside the container. Eventually, the pressure will equilibrate with the external environment, and the gas will fill the available space within the container.