= Solution
Retain the preceding \b[isothermal] assumption, so the gas <temperature> remains $T_0$. When two neutral <hydrogen> atoms become one <molecular hydrogen> molecule, the mean particle mass doubles. At fixed <mass density> and <temperature> the <ideal gas law> would halve the <pressure>, but the flowing gas is free to compress and change speed. It cannot in general keep density, <pressure>, and <velocity> all unchanged.
To describe a thin steady transition, label the atomic and molecular sides by $1$ and $2$ and neglect the integrated external force and radiative recoil across its small thickness. Local <mass conservation> and <momentum conservation> require
$$
j=\rho_1u_1=\rho_2u_2,\qquad
p_1+\rho_1u_1^2=p_2+\rho_2u_2^2.
$$
The <isothermal sound speed> changes from $a_1^2=k_BT_0/m_H$ to $a_2^2=a_1^2/2$. Dividing the momentum flux by $j$ gives $u_2+a_2^2/u_2=J$, with $J=u_1+a_1^2/u_1$. The subsonic continuation is therefore
$$
u_2=\frac{J-\sqrt{J^2-2a_1^2}}2,\qquad
\frac{\rho_2}{\rho_1}=\frac{u_1}{u_2},\qquad
p_2-p_1=j(u_1-u_2)>0.
$$
Thus the gas becomes denser and slower. In the well-subsonic limit, where ram stresses are small compared with thermal <pressure>, the useful leading description of <isothermal flow through molecular hydrogen formation> is
$$
\boxed{T_2=T_1,\qquad \rho_2\simeq2\rho_1,\qquad
u_2\simeq\frac{u_1}{2},\qquad p_2\simeq p_1.}
$$
The exact momentum condition gives a small <pressure> increase at low Mach number, rather than an imposed discontinuous factor-of-two <pressure> drop. The full expressions above apply when the subsonic speed is not asymptotically small.
Radiation of the molecular binding energy prevents that released energy from automatically heating the gas. It does \b[not], by itself, determine the <temperature>: the constant-temperature result uses the inherited isothermal closure. If that assumption is relaxed, an energy equation including cooling and molecular degrees of freedom is needed; the wording about emitted binding energy alone does not uniquely determine all four changes.
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