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A "litre" can weigh different amounts depending on what the litre is comprised of. For example, a litre of water will weigh more than a litre of chocolate mousse (more air in the mousse, but I admit the example's odd)... If you then dissolve a lot of sugar in the litre of water, it will weigh more than it did previously (the volume will also increase a little, some will have to be poured out to retain "1 litre", but it will not weigh what it did originally). So it is not possible to know how much of a litre weighs a gram without knowing what substance the litre is comprised of.
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