New R-matrix calculations of electron impact excitation rates for transitions among the 2s22p, 2s2p2 and 2p3 levels of ArXIV are presented. These data are subsequently used to derive the theoretical electron density diagnostic emission-line intensity ratios R1=I(187.95 Å)/I(194.41 Å) and R2=I(257.40 Å)/I(243.78 Å) for a range of densities (Ne= 109-1013 cm-3) and electron temperatures (Te= 106.3-106.7 K) appropriate to solar transition region and coronal plasmas. A comparison of these diagnostics with observational data for solar active regions and flares, obtained with the Naval Research Laboratory's S082A spectrograph on board Skylab, reveals that the electron densities determined from R1 are in good agreement with those estimated from line ratios in FeXIV or FeXV, which are formed at similar electron temperatures to ArXIV. However, there are large discrepancies between densities inferred from the R2 ratio and those from FeXIV or FeXV, confirming that the ArXIV 243.78- and 257.40-Å lines are badly blended with FeXV 243.79 Å and FeXIV 257.38 Å, respectively. Hence, R2 cannot be employed as a density diagnostic, in contrast to R1, which does provide reliable Ne estimates.