Problem 17 - Chemistry: Principles and Reactions

Question

A piece of dry ice \(\left(\mathrm{CO}_{2}(s)\right)\) has a mass of \(22.50 \mathrm{~g}\). It is dropped into an evacuated 2.50-L flask. What is the pressure in the flask at \(-4^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Answer: The pressure inside the flask is 4.47 atm.

Step 1: Convert mass to moles

To convert the mass of dry ice to moles, we will use the molar mass of Carbon Dioxide (CO2). The molar mass of CO2 is 12.01 g/mol for Carbon and 16.00 g/mol for Oxygen (which has two atoms in CO2), giving a total molar mass of 44.01 g/mol the\ we divide the 22.50 g of dry ice by this molar mass to find the moles of CO2: n = (22.50 g) / (44.01 g/mol) = 0.511 moles

Step 2: Convert temperature to Kelvin

The temperature given is -4°C. To convert it to Kelvin, we add 273.15 to it. T = -4°C + 273.15 = 269.15 K

Step 3: Use ideal gas law equation to find the pressure

Now, we will use the ideal gas law equation, PV = nRT, to find the pressure, P. The ideal gas constant, R, is 0.0821 L atm / (mol K). The volume, V, is given as 2.50 L. So, P = nRT / V = (0.511 moles) * (0.0821 L atm / (mol K)) * (269.15 K) / (2.50 L) P = 4.47 atm The pressure in the flask is 4.47 atm when the dry ice is dropped into it at -4°C.

Key Concepts

Dry Ice Sublimation

Dry ice, which is essentially solid carbon dioxide ((CO2(s))), undergoes a process known as sublimation, where it transitions directly from a solid to a gas without passing through a liquid phase. This intriguing property is often demonstrated in educational settings and has practical uses, such as creating fog effects or cooling substances.

When dry ice is placed in an evacuated flask, its sublimation increases the number of gas molecules in the flask, which, in turn, elevates the pressure. It's important to understand that during sublimation, the mass of the dry ice decreases as CO2 molecules escape into the gaseous form. Knowing the initial mass of the dry ice, as in our exercise, allows us to calculate the quantity of carbon dioxide gas produced using the ideal gas law, after accounting for the number of moles sublimated.

Molar Mass Calculation

Understanding molar mass is essential for converting between the mass of a substance and the quantity of its particles (moles). The molar mass is the weight of one mole of a substance, often expressed in grams per mole ((g/mol)). Each element has its unique molar mass, typically found in the periodic table or scientific databases.

To calculate

the molar mass of a compound

such as CO2, you sum the molar masses of each element multiplied by the number of atoms of that element in the molecule. For CO2, we sum the molar mass of one carbon atom (12.01 g/mol) plus the molar masses of two oxygen atoms (2 * 16.00 g/mol), equating to 44.01 g/mol. This step is crucial for converting the mass of dry ice used in the exercise to moles, which then plays a key role in applying the ideal gas law.

Converting Celsius to Kelvin

Temperature measurements often require conversion from Celsius to Kelvin, especially when working with scientific equations like the ideal gas law, which call for temperature in Kelvin. The Kelvin scale is an absolute thermodynamic temperature scale using 'absolute zero' as its null point.

The conversion is straightforward: to change a temperature from Celsius to Kelvin, you

add 273.15

to the Celsius temperature. By doing so, you account for the difference between the absolute zero points of the two scales. In the context of our exercise, the dry ice starts at -4°C, which converts to 269.15 K. Measuring temperature in Kelvin ensures accuracy when calculating pressure or volume changes in gases, as described by gas laws.