<problem>
    <text>
<p>Metallothermic production of zirconium (Zr) would involve the reaction of sodium (Na) with zirconium tetrachloride (ZrCl<sub>4</sub>).</p>

<p><b>(a)</b> Write a balanced chemical equation.</p>

<!-- chemformularesponse 
[mathjax]  \text{a ZrCl}_{4 } + \text{ b }\text{Na} -> \text{ c }\text{NaCl } + \text{ d } \text{Zr} [/mathjax]
ratio of (a, b, c, d) = (1, 4, 4, 1)
-->

    <customresponse>
        <chemicalequationinput size="50"/>
<answer type="loncapa/python">

if chemcalc.chemical_equations_equal(submission[0], 'ZrCl4 + 4 Na -&gt; 4 NaCl + Zr'):
    correct = ['correct']
else:
    correct = ['incorrect']

</answer>
    </customresponse>

<p><b>(b)</b> Write the balanced chemical equation using lowest whole numbers.</p>

<!-- chemformularesponse
as above, with (a, b, c, d) = (1, 4, 4, 1)
-->

    <customresponse>
        <chemicalequationinput size="50"/>
<answer type="loncapa/python">

if chemcalc.chemical_equations_equal(submission[0], 'ZrCl4 + 4 Na -&gt; 4 NaCl + Zr', exact=True):
    correct = ['correct']
else:
    correct = ['incorrect']

</answer>
    </customresponse>



<p><b>(c)</b> Calculate the amount of zirconium produced (in kg) if a reactor were charged with 111 kg [mathjaxinline]\text{ZrCl}_4[/mathjaxinline] and 11.1 kg [mathjaxinline]\text{Na}[/mathjaxinline].
    <numericalresponse answer="11.0">
        <responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance" />
        <textline math="1" />
    </numericalresponse> </p>
<br/>
<solution>
    <p><b>SOLUTION:</b></p>
    <p><b>(b)</b>[mathjax] \text{ZrCl}_{4 } + \mathbf{4 }\text{Na} = \mathbf{4 }\text{NaCl } + \mathbf{1 } \text{Zr} [/mathjax] </p>
    <p><b>(c)</b></p> 
    <p>[mathjaxinline]111\text{kg ZrCl}_4 = 111000/[91.22 + (4 \times 35.45)] = 476 \text{ moles ZrCl}_4[/mathjaxinline] </p>
    <p>[mathjaxinline]11.1\text{ kg Na} = 11100/22.99 = 483\text{ moles C}[/mathjaxinline]</p>
    <p>stoichiometry of reaction further dictates that on a molar basis there needs to be 4 x amount of [mathjaxinline]\text{Na}[/mathjaxinline] as there is [mathjaxinline]\text{ZrCl}_4[/mathjaxinline], but calculations show there to be a shortfall of [mathjaxinline]\text{Na}[/mathjaxinline] </p>
    <p>[mathjaxinline]\therefore[/mathjaxinline] reaction yield is contrained by [mathjaxinline]\text{Na}[/mathjaxinline] present </p>
    <p>stoichiometry of reaction further dictates that if [mathjaxinline]\text{Na}[/mathjaxinline] controls the yield, then the amount of [mathjaxinline]\text{Zr}[/mathjaxinline] produced = 1/4 x molar quantity of [mathjaxinline]\text{Na}[/mathjaxinline] = 1/4 x 483 moles = 121 </p>
    [mathjaxinline]121 \text{ moles Zr} \times 91.22\text{ g / mol } \mathbf{= 11.0 \text{ kg Zr} }[/mathjaxinline]<br/>
</solution>
</text>
</problem>


