We propose to complete an investigation of the phase diagram of a series of molecular 2D quantum Heisenberg antiferromagnets (2DQHAFs) with random exchange strengths. This is a project started at PSI by Dr Fan Xiao, where materials from the series (QuinH)2Cu(Br{1-x}Cl{x})4.2H2O with x<0.5 were successfully measured. However, in the last few weeks, high magnetic field magnetization measurements have shown surprising indirect evidence for magnetic order for concentrations close to x=1 which have yet to be measured with muons. We have shown that muons are a powerful means of exploring magnetic critical behaviour in this system and we now seek to measure three compounds with high Cl concentrations in order to complete our investigation of the phase diagram of this novel 2DQHAF.