First, we need to find the mass of argon.
This can be done using the formula rho = frac(m)(V); where rho is the density, m is the mass, and V is the volume of the substance:
Rightarrow rho = frac(m)(V)
Rightarrow m = rho cdot V
The density of argon 1.784 "g L"^(- 1):
Rightarrow m = (1.784 "g L"^(- 1)) cdot (51.0) "L"
Rightarrow m = 90.984 "g"
Then, let's use the formula n = frac(m)(M); where n is the number of moles, m is the mass, and M is the molar mass of the substance:
Rightarrow n = frac(m)(M)
The molar mass of argon is 39.948 "g mol"^(- 1)
Rightarrow n = frac(90.984 " g")(39.948 " g mol"^(- 1))
Rightarrow n approx 2.28 "mol"