Question

(b) calculate the pressure of the co₂(g) in the container at 425 k. (c) in terms of kinetic molecular theory, briefly explain why the pressure of the co₂(g) in the container changes as it is heated to 425 k.

Explanation:

1. For part (b) - Using the Ideal - Gas Law (Step - by - Step Format):

• Assume we know the number of moles of \(CO_2\) (\(n\)), the volume of the container (\(V\)), and we are given the temperature \(T = 425K\). The ideal - gas law is \(PV=nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the ideal - gas constant (\(R = 0.0821\ L\cdot atm\cdot K^{-1}\cdot mol^{-1}\)), and \(T\) is the temperature in Kelvin.
• First, we need to re - arrange the ideal - gas law to solve for pressure \(P\).

Step 1: Rearrange the ideal - gas law

We start with \(PV = nRT\). Divide both sides of the equation by \(V\) to isolate \(P\). The formula for pressure is \(P=\frac{nRT}{V}\).

Step 2: Substitute the known values

If we know the values of \(n\), \(R = 0.0821\ L\cdot atm\cdot K^{-1}\cdot mol^{-1}\), \(T = 425K\), and \(V\), we substitute them into the formula \(P=\frac{n\times0.0821\ L\cdot atm\cdot K^{-1}\cdot mol^{-1}\times425K}{V}\).

According to kinetic molecular theory, the pressure of a gas is due to the collisions of gas molecules with the walls of the container. When the gas is heated to \(425K\), the average kinetic energy of the \(CO_2\) molecules increases (\(KE=\frac{3}{2}kT\), where \(k\) is the Boltzmann constant and \(T\) is the temperature). Faster - moving molecules collide with the walls more frequently and with greater force, resulting in an increase in pressure.

Answer:

\(P=\frac{34.8925n}{V}\ atm\) (assuming \(n\) is in moles and \(V\) is in liters)

1. For part (c) - Using Answer - Explanation Format):