What volume of \(\mathrm{H}_{2}\) gas, measured at \(27^{\circ} \mathrm{C}\) and 700 . torr, can be obtained by reacting \(5.00 \mathrm{~g}\) of zinc metal with \(100 . \mathrm{mL}\) of \(0.350\) \(M \mathrm{HCl}\) ? The equation is $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$

To begin any stoichiometry calculation, it’s essential to understand the concept of molar mass. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It relates the mass of an element or compound to the amount in moles. For instance, the molar mass of zinc (Zn) in the given problem is 65.38 g/mol. This means that one mole of zinc weighs 65.38 grams. To find the number of moles in a given mass of Zn, you would use the formula: \[\text{moles} = \frac{\text{mass}}{\text{molar mass}} \] It simplifies to: \[\text{moles}_{\text{Zn}} = \frac{5.00 \text{ g}}{65.38 \text{ g/mol}} = 0.0765 \text{ mol} \] Understanding molar mass helps in converting mass to moles which is a critical step in stoichiometric calculations.

The limiting reactant in a chemical reaction is the substance that is entirely consumed first, limiting the amount of product formed. In the reaction \[\text{Zn(s)} + 2 \text{HCl(aq)} \rightarrow \text{ZnCl}_{2}\text{(aq)} + \text{H}_{2}\text{(g)} \] each mole of zinc requires 2 moles of hydrochloric acid (HCl). To determine which reactant is the limiting one, compare the mole ratio of the reactants used to the ratio required by the balanced equation. Given: - Moles of Zn required: \[\text{moles}_{\text{Zn}} \times 2 = \text{0.0765 mol} \times 2 = 0.153 \text{ mol HCl} \] - Available moles of HCl: \[\text{moles}_{\text{HCl}} = 0.035 \text{ mol} \] Since there's less HCl available than required, HCl is the limiting reactant. Knowing the limiting reactant is crucial for calculating the product's yield.

The ideal gas law describes the behavior of an ideal gas in terms of pressure (P), volume (V), temperature (T), and amount in moles (n). The equation is: \[ \text{PV} = \text{nRT} \] Where R is the universal gas constant, which is 8.314 J/(mol K). In the problem, we need to find the volume of hydrogen gas (\text{H}_{2}) produced. Given: - n = 0.0175 moles (of \text{H}_{2}) - P = 93325 Pa (convert from 700 torr) - T = 300 K (convert from 27°C) Plug these values into the ideal gas law: \[ \text{V} = \frac{\text{nRT}}{\text{P}} \frac{0.0175 \text{ mol} \times 8.314 \text{ J/(mol K)} \times 300 \text{ K}}{93325 \text{ Pa}} = 0.000466 \text{ m}^3 \] Converting cubic meters to liters (1 m³ = 1000 L), we get: \[\text{V} = 0.466 \text{ L} \] This shows how the ideal gas law is used to determine the volume of a gas.

A chemical reaction involves rearranging the atoms of reactants to form new products. In the given example, the reaction between zinc (Zn) and hydrochloric acid (HCl) forms zinc chloride (ZnCl₂) and hydrogen gas (H₂). The balanced equation is: \[ \text{Zn(s)} + 2 \text{HCl(aq)} \rightarrow \text{ZnCl}_{2}\text{(aq)} + \text{H}_{2}\text{(g)} \] The coefficients in the equation tell you the ratio of moles of each reactant and product involved in the reaction. For every mole of Zn, 2 moles of HCl are needed, producing 1 mole of ZnCl₂ and 1 mole of H₂. Understanding the balanced equation makes it easier to determine the limiting reactant and the quantity of each product formed. Always make sure to balance your chemical equations to reflect the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.