An exhaust gas control apparatus comprising: an exhaust gas control member that is provided in an exhaust system of an internal combustion engine in order to control an exhaust gas by removing a predetermined component contained in the exhaust gas, the exhaust gas control member being divided into a plurality of cells in the exhaust gas flow direction; a purifying agent supply device that supplies a purifying agent to an upstream side of the exhaust gas control member in the exhaust system so that the purifying agent is adsorbed to the exhaust gas control member and caused to react with the predetermined component in the exhaust gas that passes through the exhaust gas control member; an inflowing component amount acquisition device that obtains an amount of the predetermined component in the exhaust gas flowing into the exhaust gas control member; an outflowing component amount acquisition device that obtains an amount of the predetermined component in the exhaust gas flowing out of the exhaust gas control member; and a temperature acquisition device that obtains a temperature of the exhaust gas control member, characterized by a control device that obtains a purifying agent adsorption amount distribution through the exhaust gas control member on the basis of the predetermined component amount obtained by the inflowing component amount acquisition device, the predetermined component amount obtained by the outflowing component amount acquisition device, and the temperature obtained by the temperature acquisition device, wherein the control device controls the purifying agent supply supplied by the purifying agent supply device on the basis of the obtained purifying agent adsorption amount distribution; and wherein the control device obtains a slip determination value, which is an index for determining a likelihood that the purifying agent flows out of the exhaust gas control member, on the basis of the purifying agent adsorption amount distribution through the exhaust gas control member, and when the slip determination value equals or exceeds a predetermined second threshold, controls the purifying agent supply device to stop the purifying agent supply or reduce a purifying agent supply amount. an exhaust gas control member that is provided in an exhaust system of an internal combustion engine in order to control an exhaust gas by removing a predetermined component contained in the exhaust gas, the exhaust gas control member being divided into a plurality of cells in the exhaust gas flow direction; a purifying agent supply device that supplies a purifying agent to an upstream side of the exhaust gas control member in the exhaust system so that the purifying agent is adsorbed to the exhaust gas control member and caused to react with the predetermined component in the exhaust gas that passes through the exhaust gas control member; an inflowing component amount acquisition device that obtains an amount of the predetermined component in the exhaust gas flowing into the exhaust gas control member; an outflowing component amount acquisition device that obtains an amount of the predetermined component in the exhaust gas flowing out of the exhaust gas control member; and a temperature acquisition device that obtains a temperature of the exhaust gas control member, characterized by a control device that obtains a purifying agent adsorption amount distribution through the exhaust gas control member on the basis of the predetermined component amount obtained by the inflowing component amount acquisition device, the predetermined component amount obtained by the outflowing component amount acquisition device, and the temperature obtained by the temperature acquisition device, wherein the control device controls the purifying agent supply supplied by the purifying agent supply device on the basis of the obtained purifying agent adsorption amount distribution; and wherein a control device that obtains a purifying agent adsorption amount distribution through the exhaust gas control member on the basis of the predetermined component amount obtained by the inflowing component amount acquisition device, the predetermined component amount obtained by the outflowing component amount acquisition device, and the temperature obtained by the temperature acquisition device, wherein the control device controls the purifying agent supply supplied by the purifying agent supply device on the basis of the obtained purifying agent adsorption amount distribution; and wherein the control device obtains a slip determination value, which is an index for determining a likelihood that the purifying agent flows out of the exhaust gas control member, on the basis of the purifying agent adsorption amount distribution through the exhaust gas control member, and when the slip determination value equals or exceeds a predetermined second threshold, controls the purifying agent supply device to stop the purifying agent supply or reduce a purifying agent supply amount.