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Density of water = 1g/cm³ 
1L = 1000 cm³
mass of 1L water = density×volume = 1g/cm³ ×1000cm³ = 1000g

molar mass of water = 18g
number of moles in 1000g =  \frac{1000}{18}\ moles=\boxed{55.55\ mole}

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There are 55.55 moles per litre of water .