Is this reaction possible?
It is interesting to consider that either outcome is possible, depending on the order of addition.

If a solution containing 0.5 moles of HCl is added to a solution of 1 mole of K2CO3, slowly, with mild stirring, cold, the products will be 0.5 KCl + 0.5 KHCO3. Nothing is lost to the atmosphere.

However, if a solution of 1 mole of K2CO3 is added to a solution of 0.5 moles of HCl, it would be possible to get 0.5 KCl + 0.5 K2CO3 with slow addition, rapid stirring, warm/hot. The difference here is that the initial K2CO3 is completely overwhelmed by the HCl and produces KCl + H2CO3, which can be degraded to H2O + CO2. By the time half of the K2CO3 is added, the products are 0.5 KCl + CO2, and the CO2 could be mostly evolved as gas and disappears. The last half of the K2CO3 just comes in and sits there.