A 1.00 L flask is filled with 1.25 g of argon at 25 ∘C. Ethane vapor is added to the same flask until the total pressure is 1.050 atm .?

The total pressure (1.050 atm) is redundant.

Consider the argon gas in the flask:
Partial pressure, P = ? atm
Volume, V = 1.00 L
Mass, m = 1.25 g
Molar mass, M = 40.0 g/mol
Temperature, T = (273 + 25) K = 298 K
Gas constant, R = 0.08206 L atm / (mol K)

PV = nRT and n = m/M
Then, PV = (m/M)RT
Hence, P = (mRT)/(VM)

Partial pressure of Ar = 1.25 × 0.08206 × 298 / (1.00 × 40.0) atm = 0.764 atm