Question

gas laws fact sheet
ideal gas law pv = nrt
ideal gas constant r = 8.314 j/(mol k) or r = 0.0821 l atm/(mol k)
standard atmospheric pressure 1 atm = 101.3 kpa
celsius to kelvin conversion k = °c + 273.15
1 h 1.008
19
select the correct answer.
when magnesium reacts with hydrochloric acid, hydrogen gas is formed: 2hcl + mg → h₂ + mgcl₂.
what is the volume of hydrogen produced at 25°c and 101.3 kilopascals when 49.0 grams of hcl reacts with excess magnesium? use the periodic table and ideal gas resource.
a. 1.38 l
b. 2.76 l
c. 16.4 l
d. 32.9 l
e. 33.1 l

Explanation:

Step1: Calculate moles of HCl

The molar - mass of HCl is \(M_{HCl}=1.008 + 35.45=36.458\ g/mol\). The number of moles of HCl, \(n_{HCl}=\frac{m}{M}=\frac{49.0\ g}{36.458\ g/mol}\approx1.344\ mol\).

Step2: Determine moles of \(H_2\)

From the balanced chemical equation \(2HCl+Mg
ightarrow H_2 + MgCl_2\), the mole - ratio of \(HCl\) to \(H_2\) is \(2:1\). So, \(n_{H_2}=\frac{1}{2}n_{HCl}=\frac{1}{2}\times1.344\ mol = 0.672\ mol\).

Step3: Convert temperature to Kelvin

Given \(T = 25^{\circ}C\), convert to Kelvin: \(T=(25 + 273.15)\ K=298.15\ K\). The pressure \(P = 101.3\ kPa=1\ atm\).

Step4: Use the ideal gas law \(PV = nRT\)

We want to find \(V\), and from \(PV=nRT\), we can solve for \(V\): \(V=\frac{nRT}{P}\). Substitute \(n = n_{H_2}=0.672\ mol\), \(R = 0.0821\frac{L\cdot atm}{mol\cdot K}\), \(T = 298.15\ K\), and \(P = 1\ atm\) into the formula. \(V=\frac{0.672\ mol\times0.0821\frac{L\cdot atm}{mol\cdot K}\times298.15\ K}{1\ atm}\approx16.4\ L\).

Answer:

C. 16.4 L