Answer
Bronsted-Lowry Acid: $H{SO_4}^-(aq)$
Bronsted-Lowry Base: $H{CO_3}^-(aq)$
Conjugate Base: $S{O_4}^{2-}(aq)$
Conjugate Acid: $H_2CO_3(aq)$
Work Step by Step
$H{SO_4}^-(aq) + H{CO_3}^-(aq) S{O_4}^{2-}(aq) + H_2CO_3(aq)$
Since $H{SO_4}^-$ donates one proton, it is the acid;
Since $H{CO_3}^-$ receives one proton, it is the base;
$S{O_4}^{2-}$ is the conjugate base because it is the acid ($H{SO_4}^-$) after donating a proton
$H_2CO_3$ is the conjugate acid because it is the base ($H{CO_3}^-$) after receiving a proton.
