Effusion Rate and Temperature

The rate of effusion is the measure of the speed at which gas molecules escape through a small hole or opening. This rate is dependent on several factors, including the temperature of the gas.

Effusion Rate Ratio

The ratio of the effusion rate of two gases is determined by taking the square root of the inverse ratio of their molecular masses. This is known as Graham's law of effusion.

Mathematical Expression

For example, if we have two gases A and B, with molecular masses of m_A and m_B, respectively, then the ratio of their effusion rates (R_A and R_B) is given by:

R_A/R_B = √(m_B/m_A)

Effusion Rates of N2 and SO2

Given that we have to find the temperature at which the rate of effusion of N2 is 1.625 times that of SO2 at 500°C. We can use Graham's law to calculate the ratio of their effusion rates at any temperature, as long as we know their molecular masses.

The molecular mass of N2 is 28 g/mol, and that of SO2 is 64 g/mol. Using Graham's law, we can write:

R_N2/R_SO2 = √(m_SO2/m_N2) = √(64/28) = 2

This means that at the same temperature, the rate of effusion of N2 is twice that of SO2. However, we need to find the temperature at which the ratio is 1.625. Let's call this temperature T.

Using Graham's law again, we can write:

R_N2/R_SO2 = √(m_SO2/m_N2) * √(T_SO2/T_N2)

Substituting the values we know, we get:

1.625 = 2 * √(T_SO2/T_N2)

Squaring both sides and solving for T, we get:

T = T_SO2 * (1.625/4) = T_SO2 * 0.40625

Since we know the temperature of SO2 is 500°C, we can plug this in and get:

T = 500 * 0.40625 = 203.125°C

Therefore, the temperature at which the rate of effusion of N2 is 1.625 times that of SO2 at 500°C is approximately 203°C.

Answer: c. 110 d celsius