An automotive air-bag inflator employs the rapid decomposition of sodium azide ( ) to…

CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance

Problem

An automotive air-bag inflator employs the rapid decomposition of sodium azide (NaN3\mathrm{NaN_3}) to generate nitrogen gas. A particular inflator requires 0.250 mol0.250\,\text{mol} of solid NaN3\mathrm{NaN_3} to function properly, but the storage cartridge currently contains only 8.00 g8.00\,\text{g} of the compound. Average atomic masses (amu): Na = 22.99, N = 14.01. Address the tasks below. (a) Calculate the molar mass of sodium azide. (b) Determine the number of moles of sodium azide actually available in the 8.00 g8.00\,\text{g} cartridge. (c) Evaluate whether the available amount meets the inflator’s requirement of 0.250 mol0.250\,\text{mol}. Support your conclusion with quantitative evidence. (d) If the cartridge is deficient, calculate the percentage shortfall relative to the required amount, reporting the value with three significant figures.

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