At a certain point in a coal gasification process, a sample...

At a certain point in a coal gasification process, a sample of the gas is taken and stored in a $1-\mathrm{L}$ cylinder. An analysis of the mixture yields the followings results: Component $\begin{array}{lllll}\mathrm{H}_{2} & \mathrm{CO} & \mathrm{CO}_{2} & \mathrm{~N}_{2}\end{array}$ $\begin{array}{lllll}\text { Percent by mass } & 2 & 45 & 28 & 25\end{array}$ Determine the mole fractions and total mass in the cylinder at $100 \mathrm{kPa}, 20^{\circ} \mathrm{C}$. How much heat must be transferred to heat the sample at constant volume from the initial state to $100^{\circ} \mathrm{C} ?$

At a certain point in a coal gasification process, a sample of the gas is taken and stored in a $1-\mathrm{L}$ cylinder. An analysis of the mixture yields the followings results:
Component $\begin{array}{lllll}\mathrm{H}_{2} & \mathrm{CO} & \mathrm{CO}_{2} & \mathrm{~N}_{2}\end{array}$
$\begin{array}{lllll}\text { Percent by mass } & 2 & 45 & 28 & 25\end{array}$
Determine the mole fractions and total mass in the cylinder at $100 \mathrm{kPa}, 20^{\circ} \mathrm{C}$. How much heat must be transferred to heat the sample at constant volume from the initial state to $100^{\circ} \mathrm{C} ?$

Key Concepts

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and number of moles (PV = nRT). This fundamental principle is used to determine the total number of moles in a gas sample when its pressure, volume, and temperature are known.

Mole Fractions

Mole fractions express the ratio of moles of a specific component to the total moles in a gas mixture. They are essential for characterizing the composition of multi-component systems independently of their masses.

Mass Composition and Conversion to Moles

Percent by mass data is used to determine the mass of each component in the mixture, which can then be converted to moles using the molecular weight. This process connects mass-based composition to mole-based composition, which is necessary for applying the ideal gas law and computing mole fractions.

Constant Volume Heating Process

A constant volume process is one in which the volume of the system remains fixed while its temperature changes. In such processes, the heat transfer is directly related to the change in the internal energy of the system.

Specific Heat Capacity at Constant Volume

The specific heat capacity at constant volume (Cv) quantifies the amount of heat required to raise the temperature of a unit amount of substance by one degree Celsius (or Kelvin) at constant volume. It is used to calculate the heat absorbed or released during temperature changes in constant-volume processes.

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