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"#