Fraction appears small on the left side of the equation and large on the right side

Question

As you can see in the picture the fraction appears small on the left side of the equation and large on the right side.

Here's my code:

\documentclass[a4paper,12pt,parskip]{scrreprt}
\usepackage[T1]{fontenc} 
\usepackage[utf8]{inputenc} 
\usepackage[ngerman]{babel} 
\usepackage{marvosym} 
\usepackage{lmodern}
\usepackage{calc}
\usepackage{amsmath}
\usepackage{enumitem} 
\usepackage{tabularx}
\usepackage{siunitx}  
\usepackage[version=4]{mhchem}
\sisetup{locale = DE} 
\usepackage[intlimits]{empheq}
\usepackage{amssymb,mathrsfs}
\usepackage{theorem} 
\usepackage[pdftex]{graphicx}
\usepackage{physics}
\usepackage{nameref}
\usepackage{array}
\tolerance=2000 
\setlength{\emergencystretch}{20pt} %verhindert das herrausragen von Wörtern übers Zeilenende

\begin{document}
\begin{align*}
\log v_0&=\log k_R + \alpha \cdot \log [\ce{I}]_0 \\
$\rz{I}){ }$\log 8,70\cdot 10^{-4}\frac{mol}{dm^3 s} &= \log k_R + \alpha\cdot\log  1\cdot 10^{-5}\frac{mol}{dm^3}\\
$\rz{II}){ }$\log 3,48\cdot 10^{-3}\frac{mol}{dm^3 s} &= \log k_R + \alpha\cdot\log 2\cdot 10^{-5}\frac{mol}{dm^3}\\
\end{align*}
\end{document}

You guys have an idea why that happens and how I can make both small? Thanks in advance!

Answer 1

As Schrödinger's cat has pointed out, the problem lies with the $ inside the align environment.

\begin{align*}
    \log v_0&=\log k_R + \alpha \cdot \log \text{[Ar]}_0 \\
    \text{I)}\log 8,70\cdot 10^{-4}\frac{mol}{dm^3 s} &= \log k_R + \alpha\cdot\log  1\cdot 10^{-5}\frac{mol}{dm^3}\\
    \text{II)}\log 3,48\cdot 10^{-3}\frac{mol}{dm^3 s} &= \log k_R + \alpha\cdot\log 2\cdot 10^{-5}\frac{mol}{dm^3}\\
\end{align*}

Produces the desired output:

Whereas

\begin{align*}
    \log v_0&=\log k_R + \alpha \cdot \log \text{[Ar]}_0 \\
    $\text{I)}$\log 8,70\cdot 10^{-4}\frac{mol}{dm^3 s} &= \log k_R + \alpha\cdot\log  1\cdot 10^{-5}\frac{mol}{dm^3}\\
    $\text{II)}$\log 3,48\cdot 10^{-3}\frac{mol}{dm^3 s} &= \log k_R + \alpha\cdot\log 2\cdot 10^{-5}\frac{mol}{dm^3}\\
\end{align*}

reproduces your problem:

Note: I replaced \rz and \ce in your code with \text{...} to get your example working on my side.

Answer 2

Since you load siunits, why not use the much simpler \SI command to typeset numbers with units. I removed the *$ inside align*.

\documentclass[a4paper,12pt,parskip]{scrreprt}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{marvosym}
\usepackage{lmodern}
\usepackage{calc}
\usepackage{enumitem}
\usepackage{tabularx}
\usepackage{siunitx}
\usepackage[version=4]{mhchem}
\sisetup{locale = DE}
\usepackage[intlimits]{empheq}
\usepackage{amssymb,mathrsfs}
\usepackage{theorem}
\usepackage[pdftex]{graphicx}
\usepackage{physics}
\usepackage{nameref}
\usepackage{array}
\tolerance=2000
\setlength{\emergencystretch}{20pt} %verhindert das herrausragen von Wörtern übers Zeilenende

\begin{document}

\sisetup{per-mode=fraction}
\begin{align*}
\log v_0&=\log k_R + \alpha \cdot \log [\ce{I}]_0 \\
\mathrm{I})\;\log\SI{8.70e-4}{\mol\per\dm\cubed\per\s}&= \log k_R + \alpha\cdot \log\SI{1e-5}{\mol\per \dm\cubed\per\s}\\[1ex]
 \mathrm{II})\;\log \SI{3.48 e-3}{\mol\per \dm\cubed\per\s} &= \log k_R + \alpha\cdot\log \SI{2e-5}{\mol\per \dm\cubed\per\s}
\end{align*}

\end{document}