A closing cap for a container comprising: - an outer shell which extends along a longitudinal axis and comprises a lateral wall, which extends about the axis, in particular having a shape which is tubular and coaxial with the axis, and an end wall (302; 317), which closes the lateral wall at one end for delimiting a concavity; wherein the lateral wall is internally provided with a coupling structure, configured for removably coupling the cap to a neck of the container in such a way that the cap is movable from a closing position, in which the cap closes a mouth of the container, to an opening position; - an inner component (4; 4') positioned for closing the mouth of the container, when the cap is in the closing position, comprising a closing element (401, 401', 402) provided with an inner portion (401; 401'), which is configured, in use, for facing the mouth, and an outer flange, extending externally relative to the inner portion (401; 401'), which is configured for fixing to the outer shell; - a chamber, suitable for containing a product intended to be supplied into the container through the mouth, which is at least partly delimited by the inner portion (401; 401'); wherein the cap comprises an opening promoting assembly and the inner portion (401; 401') comprises a breakable portion, the opening promoting assembly being configured for axially stressing the breakable portion in such a way as to create a supplying outlet in the inner portion (401; 401') and to make the product come out of the chamber, supplying the product into the container through the mouth; characterized in that the outer shell comprises a spacer wall, which extends from the end wall (302; 317) and is internally coaxial relative to the lateral wall, the spacer wall being configured for making contact with the closing element (401, 401', 402) and for spacing the latter from the end wall (302; 317) defining a free space between the end wall (302; 317), the spacer wall and the closing element (401, 401', 402). - an outer shell which extends along a longitudinal axis and comprises a lateral wall, which extends about the axis, in particular having a shape which is tubular and coaxial with the axis, and an end wall (302; 317), which closes the lateral wall at one end for delimiting a concavity; wherein the lateral wall is internally provided with a coupling structure, configured for removably coupling the cap to a neck of the container in such a way that the cap is movable from a closing position, in which the cap closes a mouth of the container, to an opening position; - an inner component (4; 4') positioned for closing the mouth of the container, when the cap is in the closing position, comprising a closing element (401, 401', 402) provided with an inner portion (401; 401'), which is configured, in use, for facing the mouth, and an outer flange, extending externally relative to the inner portion (401; 401'), which is configured for fixing to the outer shell; - a chamber, suitable for containing a product intended to be supplied into the container through the mouth, which is at least partly delimited by the inner portion (401; 401'); wherein the cap comprises an opening promoting assembly and the inner portion (401; 401') comprises a breakable portion, the opening promoting assembly being configured for axially stressing the breakable portion in such a way as to create a supplying outlet in the inner portion (401; 401') and to make the product come out of the chamber, supplying the product into the container through the mouth; characterized in that the outer shell comprises a spacer wall, which extends from the end wall (302; 317) and is internally coaxial relative to the lateral wall, the spacer wall being configured for making contact with the closing element (401, 401', 402) and for spacing the latter from the end wall (302; 317) defining a free space between the end wall (302; 317), the spacer wall and the closing element (401, 401', 402).