2 mole of helium is mixed with 2 gram of hydrogen.find the molar heat capacity of the mixture at contant pressure.

To find the molar heat capacity of a mixture at constant pressure, we need to know the individual molar heat capacities of each component and the mole fraction of each component in the mixture.


The molar heat capacity at constant pressure (Cp) is given by the equation:

Cp = n1 * Cp1 + n2 * Cp2 + ... + nk * Cpk

Where:
Cp - Molar heat capacity at constant pressure (J/mol·K)
n1, n2, ..., nk - Mole fractions of each component in the mixture
Cp1, Cp2, ..., Cpk - Molar heat capacities of each component

First, let's find the mole fraction (x) of each component in the mixture:

Mole fraction (x) = Mole fraction of helium = Moles of helium / Total moles of the mixture

Moles of helium = 2 moles
Moles of hydrogen = Grams of hydrogen / Molar mass of hydrogen

The molar mass of hydrogen (H2) is 2.016 g/mol. Therefore:

Moles of hydrogen = 2 g / 2.016 g/mol = 0.9921 moles

Total moles of the mixture = Moles of helium + Moles of hydrogen
= 2 moles + 0.9921 moles = 2.9921 moles

Now we can calculate the mole fraction (x) of helium:

Mole fraction of helium = Moles of helium / Total moles of the mixture
= 2 moles / 2.9921 moles

Next, we need to know the molar heat capacities of helium (Cp1) and hydrogen (Cp2). The molar heat capacity of helium (Cp1) is approximately 20.786 J/(mol·K), and the molar heat capacity of hydrogen (Cp2) is approximately 28.836 J/(mol·K).

Now substitute the values into the equation to calculate the molar heat capacity of the mixture at constant pressure:

Cp = n1 * Cp1 + n2 * Cp2
= (Mole fraction of helium) * Cp1 + (Mole fraction of hydrogen) * Cp2

Cp = (2 moles / 2.9921 moles) * 20.786 J/(mol·K) + (0.9921 moles / 2.9921 moles) * 28.836 J/(mol·K)

Calculate the resulting value to find the molar heat capacity of the mixture at constant pressure.