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There is no equivalence.
A gram is a measure of mass. A quart is a measure of volume. The two measure different things and,according to basic principles of dimensional analysis, conversion from one to the other is not valid.
If you are not convinced, consider a quart of air. How many grams? Next consider a quart of water. How many grams?
The masses of equal volumes of the two substances will clearly be very different. So there is no direct conversion between mass and volume: you need to know the density of the substance to enable you to carry out the conversion.
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