If helium added to the mixture increases the pressure to 1.90 {\rm atm}, what is the partial pressure ({\rm atm}) of the helium?

To determine the partial pressure of helium in the mixture if the total pressure of the mixture is 1.90 atm, you need to know the mole fraction of helium in the mixture.

The mole fraction of a component in a mixture is the ratio of the number of moles of that component to the total number of moles in the mixture. It is represented by the symbol "χ" and can be calculated using the following formula:

χ = n_he / n_total

Where:
χ = Mole fraction
n_he = Number of moles of helium
n_total = Total number of moles in the mixture

Once you have calculated the mole fraction of helium in the mixture, you can determine the partial pressure of helium using Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases.

Mathematically, it can be expressed as:

P_total = P_he + P_other

Where:
P_total = Total pressure of the mixture
P_he = Partial pressure of helium
P_other = Sum of partial pressures of the other gases

In this case, since we are given the total pressure (P_total) and we want to find the partial pressure of helium (P_he), we rearrange the equation to solve for P_he:

P_he = P_total - P_other

Therefore, to find the partial pressure of helium in the mixture, you need to know the mole fraction of helium and the total pressure of the mixture, and then apply Dalton's Law of Partial Pressures and the equation mentioned above.

1.90