To find the mass of [tex]\( N_2(g) \)[/tex] produced in the given reaction, we can use the law of conservation of mass. This principle states that the total mass of reactants must be equal to the total mass of products in a chemical reaction. Therefore, we can set up our calculation as follows:
Given:
- Mass of [tex]\( H_2(g) \)[/tex] = 1.0 grams
- Mass of [tex]\( NO(g) \)[/tex] = 15.0 grams
- Mass of [tex]\( H_2O(g) \)[/tex] = 9.0 grams
We need to find the mass of [tex]\( N_2(g) \)[/tex].
According to the law of conservation of mass:
[tex]\[ \text{Total mass of reactants} = \text{Total mass of products} \][/tex]
Let’s denote the mass of [tex]\( N_2(g) \)[/tex] as [tex]\( \text{mass}_{N_2} \)[/tex].
Since [tex]\( H_2(g) \)[/tex] and [tex]\( NO(g) \)[/tex] are the reactants, and [tex]\( H_2O(g) \)[/tex] and [tex]\( N_2(g) \)[/tex] are the products, we can write:
[tex]\[ \text{mass}_{H_2} + \text{mass}_{NO} = \text{mass}_{H_2O} + \text{mass}_{N_2} \][/tex]
Substitute the given masses into the equation:
[tex]\[ 1.0 \, \text{gram} + 15.0 \, \text{grams} = 9.0 \, \text{grams} + \text{mass}_{N_2} \][/tex]
Now, simplify this equation:
[tex]\[ 16.0 \, \text{grams} = 9.0 \, \text{grams} + \text{mass}_{N_2} \][/tex]
Subtract 9.0 grams from both sides to solve for [tex]\( \text{mass}_{N_2} \)[/tex]:
[tex]\[ 16.0 \, \text{grams} - 9.0 \, \text{grams} = \text{mass}_{N_2} \][/tex]
So,
[tex]\[ \text{mass}_{N_2} = 7.0 \, \text{grams} \][/tex]
Therefore, the mass of [tex]\( N_2(g) \)[/tex] produced in the reaction is [tex]\( \boxed{7.0 \, \text{grams}} \)[/tex].
